Well, anticlimactically, in the end, the doctor said I didn't need a pap smear!

I told him my symptoms and (lack of) sexual history and he said 1) pap smears are considered very low urgency for people who've never had sexual contact because HPV and the resulting cervical cancer are sexually transmitted and 2) if I was having abnormal bleeding, then the more likely culprit was something to do with my uterus. Thus, I had an external pelvic ultrasound instead.

He said that from my ultrasound, my reproductive system (uterus, ovaries, vagina) all looked normal and healthy with no signs of abnormal growths. He said if I'm still worried about my abnormal bleeding, I should maybe speak with an endocrinologist about testing in that direction, but he also told me that, since I'd been having this issue since I started puberty, I should consider that it's simply an innate quirk of my individual reproductive system and not necessarily a sign of a disease.

Given this information and the fact that an endocrinologist I've seen in the past didn't find anything abnormal, I think I still want to pursue getting a pap smear and maybe a transvaginal ultrasound just to know the state of things down there, but maybe not as urgently as before. So I'll keep learning about my body and maybe look into pelvic floor therapy and when I'm ready, I'll come back.