You didn't say whether you were attracted to her in a romantic way or not, although you only mentioned friendship? I've been through exactly this on a number of occasions in the past where the person effectively became my special interest, but for me it's always been a romantic interest too, although this can still happen for some autistic people even if this isn't the case as I will explain in the next paragraph. For the past 15 years or so this has been suppressed however and I feel better off single, but I have found these obsessive thoughts virtually impossible to break in the past, they can if you're not careful frighten the person away or much worse if the person is that way inclined they could use it to take advantage of you which has happened to myself too. It's good that you seem to be trying to limit yourself so you don't appear so obsessive, but I suspect it could still come across that way if you're not really careful. You also sometimes need to be a little careful that any obsession never crosses the line into stalking, I later realised when I was much younger and still at school that I did cross the line when I started remembering the timetable of the girl I was obsessively interested in so I could "accidentally" keep being there when she left class if I was able to make it in time from my class to intercept her on her route to her next class, back then I honestly didn't understand that it was wrong, in fact I even believed that she'd be impressed at my dedication once she noticed and I hoped she'd make a move on me because I didn't have to confidence to, but it obviously ended really badly. I learned from my mistakes however and at least know not to cross what can be a fine line now.
I have a friend who I suspect is autistic and he is often obsessive even over friends that could be both male or female of any reasonable age, he doesn't even have to be sexually attracted to them to be very obsessive over them and he constantly wants to call or message them, wanting to know what they're doing all the time, then he goes on and on about them alarmingly even if they for instance don't answer the phone on one occasion and I know he has lost friends that way, but he can't seem to see it. He even pressures me to be there with him all the time and he gets upset if I'm not there to obsess, especially if it's a time I'm usually there and I find it difficult to say "no" which is one of my autistic issues I struggle with. He is a really good friend in many ways and I enjoy his company in moderation, but he is definitely obsessive and it becomes overpowering where I'm constantly fighting to get the freedom to do other things on my own as well and I can understand why some people block him out, in fact it's worse for me because I am happy to be alone more than most people and that's when I feel most comfortable (well I have my cat and she is great company). Also when I spend time with him our autistic traits clash, for instance, I am told that I often shout even though to myself my voice level sounds normal, he seems oversensitive to sound and this really irritates him and he also often complains when I go on about things because he wants peace and quiet, I offer to leave him in peace, but he doesn't want this either, so I can't win.
I would love to hear of any way to actually handle these obsessive feelings if they occur or even ways to stop them happening in the first place, whether they're related to a romantic interest or just a friend, obviously without taking harmful medications which is sadly many doctors so called "solution". Such obsessive romantic interests have only ever ended in severe heartache for myself and at least they've been suppressed now, although I've only been at the receiving end of an obsessive friendship.
PS: If you are romantically interested, if you only try to be friends, she may only ever treat you this way and it maybe too late when you finally tell her you want more. I used to find it easier to tell women I was truly interested in sexually that I was only interested in friendship because it was easier for me to handle and more comfortable, but I found out the hard way that often before long they could only ever see me as a friend which and they wouldn't want to risk ruining it with a sexual relationship. If however I showed romantic interest or at least made no mention of wanting just friendship, sometimes things would progress further than just friendship.
