Hello, Nacho.
I'm self-diagnosed, as well...though I have been for assessment more than once, and each time failed to rate as an Aspie. I'm no less convinced that I am one, however, and my situation is fairly common. Lucky for you, you're still young enough that making the 'call' could be a bit easier.
The older we get, the more difficult it can be for clinicians to reach a firm determination. One reason for this is that many of us adapt our behaviours over time, as a matter of survival, which can make us seem less 'Aspie' than we actually are. Another is a pitiful lack of adequate instruments for assessment of adults. Still another, as you may soon find out, is that the diagnostic process isn't standardised...different doctors use somewhat different methods to reach a conclusion, and there is a good deal of subjectivity involved.
For a start, if you haven't already done so, take a look at the current diagnostic criteria from the manual used in your country [the DSM-V in the U.S., or the ICD elsewhere]. This will give you a clear picture of what your doctor will be looking for, and the standards you'll have to meet for diagnosis.
You should attend your first appointment expecting a series of questions about your thinking and behaviour, which will be based on the current clinical criteria, and may also include enquiry for lesser traits typical of Aspies. You will also be asked quite a bit about your childhood...since doctors do realise that many of us make adaptations as we age, understanding how your symptoms presented when younger is essential. Beyond that, we tread into the realm of 'depends on the doctor'. Some will render a judgement in a single visit, and do little more than what I've just described. Others may have you back for several sessions and a more complicated programme.
This next bit is important: While you are, in fact, seeking the expertise of a professional, you'd do well to view yourself as an active part of the process. If you believe you're an Aspie, bring evidence to support your case...results of online self-tests, personal notes about why and how you fit the Aspie profile, letters from family members who can affirm your statements about childhood presentation, highlighted bits from books and articles that you feel describe you especially well...whatever you can offer to justify your claim. Your doctor knows medicine and psychiatry, but only you know you.
I hope this was useful. Good luck with your journey on this.