Courage to call the GP and ask for assessment

Hello everyone.

today I finally found the courage to call my GP to ask if I could book and appointment with a doctor to see if I could be referred to have an autism assessment. 
it didn’t go well at all. The person on the phone asked if it was my child who needed one and I said no, that was me, and her reaction was “reallyyyy?” She asked me how old I was, I told her I was 28 and she asked “and you want an assessment just now?”. Anyway, she told me they were fully booked, and I completely understand, and asked me to call again next week to see if there was any appointments available.

the problem is, I felt really embarrassed. It took me a really long time to find the courage to make this call and I tried every other way to make this appointment through the app or website and there is no way. 
I find very difficult to call people and after this embarrassment there is no way I will call them again next week.

I really wanted to see a doctor as my social issues are starting to affect my life.

does anyone else has a suggestion or advice? I don’t have anyone to call on my behalf. 
thanks for reading this.