If you're on methotrexate, you shouldn't get a perm. Most reputable hair stylists won't give you one. I was wanting one a year or so ago and after letting her know about my meds, she said absolutely not because she could not guarantee the outcome.

I wouldn't advise doing a perm. Over time, methotrexate makes your hair very dry & often causes hair lose. Getting a perm or coloring your hair will make it worse.