I just looked up Brown Syndrome. Cleveland Clinic web page says is a form of Strabismus and usually temporary. However, it seems like your experience is not going away and pretty severe.

I was born with Strabismus - esotropia (eye turn in) and Amblyopia (lazy eye). Had successful surgery as a toddler in one eye only many decades ago.

During the recent Pandemic, I started experiencing the same as you and eventually had the eye turn in and severe double vision (side by side and up) in certain gazes. I had specialized testing and then was referred to a Pediatric Ophthalmologist even though I was 64! Only about a dozen Specialists in my entire State.

I was diagnosed with Hypertropia (eye movement upward) and Esotropia (eye turn in). The diopter measurements were too severe for prisms to correct. Beginning of this year, I had surgery on both eyes.

Surgery took about 2 1/2 months later until I had a good result. No more double vision, eye turn, and only a tiny bit of distortion at far gazes. Since last April, I have been able to drive easily again.

I am reading that Brown Syndrome is normally treated more conservatively, but your double vision seems extreme. I went through AAPOS site to get to my testing center then was referred out for further evaluation. There is a find a doctor link on top left hand side:
https://aapos.org/glossary/brown-syndrome