Kayla, first off, can I give you a big hug?

Attempting to come out to them last year must have been incredibly hard. I'm saddened that they wouldn't believe you, but that is probably because they are scared to confront this and would rather just deny it. You need to be firm with them. Tell them you want to see a therapist. You don't necessarily have to bring up gender dysphoria if you don't want to. You can say you've been going through bouts of depression and high anxiety.
If gender dysphoria does come up though and they try to invalidate it or shrug it off... just stand your ground and tell them yes, this is what you are going through and
it is real.
Gender dysphoria is no joke. There are surveys that have shown that 41% of transgender people have attempted suicide at some point in their lives. Tell them you feel trapped and alone because you tried to tell them before and weren't taken seriously. Having a therapist, someone you can talk to who isn't going to judge or project their own beliefs or opinions on you, but will in turn listen and help you understand and explore your feelings--that is what you need right now.
If your parents still refuse then I'd start searching online, specifically for therapists who have dealt with transgender issues. Reach out to them. Try and get them to send your parents a letter on it. Maybe if they hear it from a professional then it will sink in a bit better. I don't know what else to say. It is a tough situation. Do you even have a car yet or are you still completely dependent on them? If you do have a car and a little cash you still might be able to get a therapist to see you on your own. I know plenty that work on a sliding scale depending on what the client can afford. Explore all options. When a roadblock is put before you then find a way around it.
Hang in there, I know you'll find a way to get the help you need eventually.