Hormonal migraine symptoms or something else? Which specialist should I seek?

32F - I'm facing a mix bag of symptoms that I have visited urgent care for, but they shrugged me away and said it was probably a bad migraine. I'm at a loss of where to start to try and find a better diagnosis, or even how to describe what I am feeling succinctly so a medical professional could direct me. If you kind folks could help me at least use the right jargon so it doesn't sound like I'm downplaying my issues, I'd really appreciate it.

Context - Asian, 4'11'', medically obese. I have been diagnosed with ecxema, anxiety, depression, and insomnia. I currently take escitalopram and buproxi... something for the first two. I also take a progesterone birth control. For my skin, I take Dupixent. I also have been on Wegovy and am increasing my dosage slowly to the weight loss dosage. Listing medications in case this may provide context to some side effects I am unaware of.

My cycle is very regular, and for a long time I did not take any BC pills (I stopped because they were enhancing my mental health issues). However, I started to get debilitating migraines - ones with NO aura, just searing pain and nausea and light sensitivity - around the time my hormones were highest. At first, it was during the pre-menstrual few days. Then, also during ovulation. My OBGYN put me on the progesterone BC and it sort of lessened the severity of it.

Since my last cycle, though, I have had this.... weird dizziness? It onsets suddenly. It hits harder when I close my eyes and hang my head down. It's like suddenly someone took the room I'm in and gave it a little swirl, and stopped it abruptly, so my brain is catching up or lagging, but it's NOT like the brain zaps for depression medication withdrawal. After a bit of this, nausea came. These 'swirls' wouldn't last very long. They pulsed throughout the day, every few minutes or so, and also occurred during a hormonal high. Is this vertigo or should I describe it as something else?

The pattern is that during my hormone peaks, I'd feel bad, and for the last couple of years, it's gotten worst. I don't know if it's just a coincidence though:

Just cramping -> Migraine (only during PMS) -> Migraine (during ovulation and PMS) -> Migraine during both peaks, and other new migraine(???) symptoms I had never experienced before:

• Vertigo (???)
• Extreme skin sensitivity, like any light touch feels painful, but only on my upper arms and hands. Also, temperature sensitivity - hot showers now feel like lava in these 'sessions'.

Last time, urgent care told me it was a migraine aura - not a visual-ish one, but a sensational one. I just rested and it sort of went away after a while.

QUESTIONS:

1. Is this a question to my primary care? Or is it seemingly more dire and I should seek a specialist immediately? I do coincidentally have appointments with my psychiatrist, then OBGYN, then primary care in the next month, but I don't know if this is abnormal enough to seek immediate care.
2. Is that dizziness sensation I described vertigo?

Thanks in advance. I read the rules and I hope I followed them all here.