It depends on what kind of cyst you had, but unfortunately you can totally have another one again. I had this happen to me: my cyst burst in February then I got another one that caused me issues in March. Although it is scary, I think it is worth it to go see an obgyn. Typically, those kinds of more private exams are strongly recommended, but they can't force you to do them. If you are open with your doctor from the beginning, they can help avoid any unnecessary checks as well as make you feel more comfy if you do end up having any sort of pelvic exam/ultrasound.

You can always opt for a pelvic ultrasound instead of a Trans vaginal. It's much more private and you can refuse the Trans vaginal. Don't let them pressure u to get one.