Even if you're busy for the next month and a half, it's likely that the first appointment will be that far away at least. Its nice to know for sure either way, so start calling around now

There's a website called embrace-autism.com that helps with diagnosis. It's made by a autistic woman who's plan is to help other autistic people. There's also CARD, Center for Autism and Related Disorders. If you are in the USA I would recommend that as I know they are in 27 states. I do not know if they are anywhere else but it wouldn't hurt to look.

Getting tested can be a long process as an adult, as most autism specialists focus on children. Listen to @Tired247 and their info.. I'm sure you could find someone to set an appointment with. If you think your sister will talk you out of it, I recommend keeping her out of it and only talking about it to whichever family members are supportive.

It can take months or longer to get an appointment for a formal diagnosis - if you feel like you need or want a formal diagnosis it may be worth considering it takes a while to pursue sometimes. (Not always! I got an apt in about 2 months and my insurance covered most of it and I was believed completely by thr psych as a 29yo female.) I haven't told my family. I think they would weaponize it against me as a way of explaining anything they didn't like about me. Sometimes your family won't be supportive. I'm really sorry about that. Try to not let them talk you out of pursuing something you need for you tho.

It’s worth mentioning getting tested it not a quick thing. For me, the whole process has taken over a year and $5000 from first suspecting and I get my results next week. (I’m in the US but it seems like most country’s have long wait times)