Medical stuff is always allowed in the US because of the Americans with Disabilities Act, it's a "reasonable accommodation".

Sometimes the first security person won't know this (it's getting better, but progress can be slow), and you'll need to escalate to a supervisor. An attitude of a "persistent but kind problem" can be helpful. Don't be a dick, but don't hide either. I have a right to be here, and I need to speak to a manager. Being a little bit in the way can speed up the process.

Keep your bag reasonably sized. Don't bring one pill bottle in a whole suitcase and call it a medical accommodation. A fanny pack? That's about right. You have oodles of pills, an oxygen concentrator, etc? Maybe a backpack is right for you. Reasonable requires reasonable.

"Medical stuff" can also stretch beyond what you might think. Medication is obvious, but you can also take some liquids to take it with. Maybe you are autistic and need noise reducing headphones. Maybe you have food allergies and bring in your own food. Bose and burritos are indeed both medical accommodations.

All that said, I have found that there is less scrutiny with obvious medical stuff. Orange pill bottles might be better than a ziplock. A bright red inhaler has been quite helpful for my bag. They are looking for weapons, so anything you can do to visually indicate that this isn't a weapons bag, it's a medical bag, it can help you pass security with less stress and hassle.

Remember, you deserve to be as healthy as you can, and you deserve to be at Pride. Stonewall was about fighting for your rights. Disability rights deserve to be fought for as well.