I once got a perm in an attempt to get my 3a hair to corkscrew curls.
It failed, and left my hair extremely damaged. I also had a friend with straight hair who got a perm, professionally done, which did nothing but damage her hair's structure: not a single curl. I wouldn't risk it if I were you, but it is your choice. Permed hair is a lot of trouble, and it may just be easier to set it in rollers (soft so they won't hurt your head) at night instead. Just some thoughts to consider
Dense but fine and delicate 3a hair. Feels like a dandelion without product. Difficulties in getting less puff and more definition when short.
On a mission to grow out after my big chop!