Phobia at work

I just got a new job and part of it is cleaning restrooms. The trouble is I have a big phobia of public restrooms. I haven't been in one in years. Obviously no one WANTS to clean a restroom but I truly can't even step foot in one without extreme anxiety. I don't know what to do because I can't really ask not to do it because like I said everyone wants to have an excuse not to. I would love to be able to but I can't even imagine having to go in one every day. Is there a legitimate way to get out of it or do I have to suck it up or quit?

Is it the fact that it's cleaning bathrooms or that it's public?
If it's the public aspect, would it cease to be in use when cleaning?

Are there other people who could do that part of the job? If so, you might be able to request a reasonable accommodation under the ADA (Americans with Disabilities Act). I think that there would have to be a way for the bathrooms to get cleaned without you having to do it. You would have to do some research.

It's fear of contamination. Especially bad because it's a public place and strangers.

I think you’ll have to either do it or find another job. Most employers don’t care about anything except the work getting done...

I second that. Was that something you were made aware of as a responsibility during the hiring process?
Doesn't sound like a good fit for employment. Do they at least provide face masks and heavy duty gloves?
I would say it sounds queasy, but it was actually part of my first getting money into my own bank account pre filing divorce papers jobs. And one night, I tackled the mens room. Those bathrooms maintained a near spotlessness when I was there. Men's rooms are dirtier due to the spray factor, in my experience. Kind of like being at home with sons.

I didn't know before employment. I've had this job title before and didn't have to do it at the other place so I assumed not here either. I'll have to think it through to see if I can do it but I'll either have to pretend or quit. I know I'm not ready yet to get over my fear in a week.

I ask about if it was known thinking in terms of how it could be argued as a case with unemployment. Becausebif it's not spelled out in a written contract and not known prior to job acceptance and with now as you say not previously required....then yeah...if you need to quit it could take 5-6 weeks to argue a claim.
In my current employment it would be considered something worth a grievance over..

I would add. Don't just quit without trying to resolve it first. And if it comes down to quit or be fired, maybe even better of chances.
Why would they change policy and procedure mid stream anyways? Do you feel picked on for this request? Who did it before?