Your parents are correct that many teens have hormonal mood swings that can look like bipolar disorder. But that doesn’t mean that something more serious isn’t going on. An evaluation by a mental health professional is needed to sort it out.
I’m concerned that you mention that you were diagnosed with an anxiety disorder, but you don’t mention being treated for it. I hope you have worked with a counselor to learn coping skills to help you manage the anxiety. That would go a long way toward helping you settle down if your issue is merely normal teen stuff.
The person who diagnosed you in the first place would be a place to start to get answers now. That doctor has seen you before so will be able to determine if anything has changed. (And no, therapists do not laugh at or dismiss anyone’s pain.) You might try asking your parents if you could see that doctor for a follow up visit — just to make sure you are doing okay. That may be easier for them to consider than another diagnosis.
I wish you well.