I think it's a bit of both really. I last got travel sickness about ten years ago and that caused me a fear of sickness Emetophobia, which is when the travel anxiety began. But now as well as being scared of getting sick I'll also scared of needing the toilet, and after a car crash in 2016 I'm sometimes afraid we'll be hit again.
For what it's worth, I have that same phobia, always have. So I can emphasize with what you go through on that one.
Aaaaaaaaaaanyway.
On the note of travel: I can get bad anxiety, but other times, I cant. It seems to heavily depend on the travel method.
Like, planes for instance. I have no fear of flying itself. What I dont like is the experience of having to deal with everything with no real choice. Once you're on a plane, you're locked in that stupid cramped flying tube until it reaches your destination. It's not like you can just go "Hey, pull over at this cloud here, I wanna get out and stretch my legs". You're stuck in that awful sardine can full of idiots for the duration. I dont even want to deal with people at the freaking gas station... I sure as heck dont want to spend 2 hours in a giant flying Pringles can with 100 of them all smashed together in tiny little seats.
But also, the airport. Ugh! I hate it! So many people, and the structure of the whole thing is just so stupid. And so many strange rules. And I cant deal with strict schedules. I just cant.
What's worse is I also have this bizarre phobia of having to use the bathroom in some public place. I haaaaaaaaaate that. I know, for many people it's just something they do every day, no problem. But dangit, I like some blasted privacy, yeah? How am I supposed to handle doing that in a room filled with like 10 other people? Or even worse, in the cramped bouncing mess that is the bathroom on a plane? Yeah, there's nobody in there, but with my screwy back/neck problems, that weird cramped room can be a genuine physical issue for me.
Here's the thing though: That's specifically just plane travel. CAR travel is different.
I drive every day. Not that I HAVE to.... I dont. I dont work, so there's no obligation. But if I dont get out of the house and go somewhere at least once per day, I shall surely go mad. I go to the gas station to get my fountain drink (caffeine.... my one real vice) and/or go to the store to get whatever. Or sometimes I'll go to my mom's house... or maybe I'll just drive around randomly. Heck, I know all the roads around here not from reading maps, but simply by going "ooh, I wonder where THAT goes?" and just driving down said road to see what happens.
And it's the same for the convention trips I do. Which usually involves anywhere from 1-4 hours of driving, ending up in some hotel somewhere. Now, I dont really LIKE doing super long drives, but.... eh. There's no strict schedule I have to deal with, I can stop and get out whenever I feel like it, and I'm the one in control of the vehicle... not someone else.
Anyway, as for your fear and sensitivity, one thing I might suggest is to sort of take it slow, and push a bit further each time.
For instance: get in the car, and have a very short drive. Go around the block. Go around two blocks, maybe. And then that's it. Next day, do that again. Feeling a bit more comfortable with it? The last couple of times werent a problem? Add another couple of blocks, another 5 minutes of driving/riding/whatever.
Yes, I know it's tough to do that sort of thing, but believe me, it can be worth it.
It's kinda like when I got into virtual reality about a year ago. I was real interested in trying that out, and was getting a new computer fit for it. But I'd never done it before, and there's all those awful stories of people getting sick just from using it. Wanted to try it, but at the same time, was scared of it.
What helped was research. I read up on it, learned everything about how it worked, what to do and what not to do for first time use, and things like that. The trick with VR is to not have it moving you inside the simulation. Like, so you arent sliding around like you would in some FPS game. That's what triggers people (in fact, alot of the way that problem happens is very similar to what happens to some people with riding in cars). Most VR programs feature teleportation instead of smooth locomotion for that reason. So I figured... okay. I'll avoid that. Take it slow.
Went to the Microsoft store where they had a demo setup, went in there, put the headset on. Quite nervous. But I knew what the program they were using was (since I'd looked that up too) and what to expect. No wild movement, just a calm simulation where you can mess around with things.
...Or that was the idea. Accursed thing bugged out *immediately*. Within less than a minute, the glitch hit, and I was violently thrown THROUGH the nearest wall (inside the simulation, obviously I didnt fly through the store wall, that'd be silly). I remember I just completely froze up.... until I realized I was just fine. Wasnt feeling weird or dizzy. STARTLED and nervous, sure, but nothing else. And that's when I realized: Alot of the fears I'd had really were just in my mind. And it was that mentality that was the problem... not the device.
Bought the thing, took it home. Over the next month, I used it constantly, pushing things a bit further each day. Now, I can handle anything it can throw at me. I had one point where this game I was playing bugged out while I was in it, and just started spinning me around wildly. Would have scared the heck outta me early on... but my reaction at that point was just something like "UGH I have to waste time fixing this, dont I". That early fear was gone.
Yeah, I know, VR isnt a car ride, but it DOES share some of the same properties in terms of how the "sickness" aspect can caused. And as I tell people frequently, anyone CAN get used to it and handle it... they just have to be careful about how they do it, and take the proper approach. But moreso, they have to have some faith in themselves. "I can handle this" is something that I need to hear from anyone that intends on putting that thing on for the first time, before I'll let them do so. If they're getting too nervous, well, they dont get to try it until they can get into a better mental state. Because seriously, that's important.
And it's the same with cars. You gotta go into it with the mindset of "Okay... just a bit today. I can handle this, I really can". Then get in, roll around a parking lot or whatever for 10 minutes, and then you can go "you know what... that really wasnt so bad. I was worried for nothing".
It's important to stop thinking about how worried you are. Instead, start thinking about the fact that you CAN handle it, if you take a careful, logical approach, instead of a paranoid one. It's not like you need to be learning to handle a 200-mile drive in the span of a day. But little by little, you really can do it.