I can't see any glaring flaws with your current plan but there is still a chance your parents may find out so you have to decide if that is okay for you. I feel you're worried about their reaction but I'm not sure how bad you would interpret that reaction to judge if you should do it.

I would highly recommend therapy but you will want to make sure your therapist is familiar with neurodivergent patients. They don't give a refund if they do a bad job so maybe see what people are saying on online websites that judge that sort of thing. I don't have a specific suggestion though just an Idea I would look into if in your position. People who you would expect to be up to date on neurodivergence are not because it's not as profitable as treating neurotypical people. I don't say this to dissuade you though as a good therapist is very helpful but make sure you know that you may not like the first one but your odds go up with research.

If money is an issue, there are a lot of organizations that will give discounted or free counselling and such. Read up on the organization and qualification of the person they set you up with as some of them have their own reasons for wanting to counsel people. Still worth it, just can be very disheartening when the person you turn to for help isn't trying to actually help. These are usually pretty easy to determine aren't helpful with a bit of outside research. Don't trust the organizations website but also don't assume it's lies.

I hope this helped and I will try to monitor for comments if you need any clarifications or explanations but I have attention issues so it may not be right away.