If your medical team has not diagnosed you with any conditions and/or expressed any concerns that would necessitate avoiding the gym, then I say YES - go to the gym!
The mind-body connection can make us sensitive to stimuli physically, mentally, and emotionally. I couldn’t even drink a half glass of wine without serious nerve pain, visible rashes and twitching, headaches, etc. Now I drink half a bottle of wine every Friday and Saturday night with no problem. Nada, nothing. I should’ve listened to my favorite neurologist sooner when he said I didn’t have alcoholic neuropathy at 26 years old - my body was simply in fight-or-flight mode and overreacting to stimuli.
I want to emphasize that this problem of mine didn’t go away in a single day. I continued to get symptoms after I started drinking 1 to 2 glasses of wine (6 oz per glass - I’m not one of those winos drinking single glasses as big as a bottle

). I had to truly believe I was safe and not experiencing symptoms from nerve damage. This belief allowed the symptoms to fully dissipate over the course of a couple of weekends. This was also the case with medical cannabis, but I trusted cannabis so much that the symptoms discontinued without real any effort on my part - not fearing the natural green plant made all the difference. Alcohol, however, terrified me given what I’d read about alcoholic neuropathy. Although I wasn’t an alcoholic, the nerve pain I was experiencing was shocking and seemed unexplainable. Once I understood that the symptoms were simply the result of an overactive sympathetic nervous system and not dangerous, I was on the path to becoming truly free.
Working out has so many wonderful effects on our emotional health. Try to focus on the endless benefits of exercise. You’re getting stronger, not weaker! Eventually, you’ll retrain your brain to stop going over potential dangers that (I’m assuming) no medical professional has flagged for you. Practicing mindfulness during and after exercise should also help. But given your fear of physical symptoms, I would refrain from focusing on how you feel and instead observe the objects around you, colors, sounds, etc.
You clearly enjoy working out. It would be a shame to deprive yourself of that. Just like it would be very sad for me to never enjoy a few glasses of red wine again. We can’t let our fears take everything away from us! Remember that balance is everything. Continue working with your doctors on any disordered eating. You should feel positive about the fact that you have a collaborative team looking out for you. They aren’t going to let anything happen to you!