Apparently Physical Disability in the Medical Field in a No-No

I have a really stressful problem at college. I’m in a medical program (not doctor-related tho), but I’ve been getting a lot of flak from my teachers/instructors over my essential tremor. I made a huge mistake by mentioning it at all the first semester in order to dissuade any concerns about my shaking and being nervous (“Ah, it’s just a neurological thing. NBD”). This is what I normally say in this type of situation; I’ve had this condition my whole life, so it’s pretty mundane to me. Instead of leaving me alone, they’ve had several meetings where they ask “are you sure that this is the career for you”, try to psych me up about how some of the procedures and techniques are super difficult, and how “you could kill a patient with one mistake”. Helpful, especially for my self esteem. My tremor is annoying at worst, and looks terrible from a rando’s view, but is honestly not a significant problem.

Now, without going into any specifics, anytime I make a mistake, they jump to conclusions and assume it happened because of the tremor. I’ve only made 2 mistakes so far, none of them severe. None of mistakes I’ve made have been due to my tremor; all of them have been freak accidents, because of course I’m the one that happens to be there when the crap hits the fan. I'm certainly not disregarding my mistakes, as I do not want them happening in real life, and it is a good idea to practice so that I know what to do next time I get into such situations.

My tremor has not prevented or even hindered me from completing any of the skills, and has not actually caused any problems or mistakes, so I don't know why they're freaking out so hard about it. They’re also pressuring me to disclose my condition during clinicals “because it’s a liability”. I do not want to do this because:

-I do not require any special accommodations.

-It's not a liability because it has not caused any problems; only being a clueless noob has. Certainly none of the other students have Clueless Noob Syndrome.

-I do not want more people acting like my teachers. It’s anxiety-inducing, which only makes the tremor worse.

-According to college policy (and ADA I think), no one can disclose any information without my consent (this has not stopped my teachers from telling all the other teachers in the program without my permission), but there’s always the possiblilty of a Freudian slip or self-righteous person, and since people in this field tend to communicate, I do not want to sabotage my career before it’s even started.

I feel like my teachers are prejudiced towards me, and it's really upsetting. Am I justified for feeling so? Is there anything I can do?