My 3 year old son is scared of public restrooms also. I have to keep telling him that everyone is doing poopie and peepee and that it's ok. I go in the stall and hold him on the potty while I squat down so he can hug me around my neck. That's the only way he'll go. I think it might help if you bribe him or let him bring a small toy in there. I'm not sure but my son loves washing his hands (aka playing in the sink with soap) so I just promise him after he goes potty we can wash hands. Maybe there's something similar you can do with your son to make him see the restroom as a positive place.
Momma you're not alone! My Son is 3 and will do great naked at home. Will only pee at daycare, won't tell them he has to go or wants to go. Underwear he just wears wet. He also will not stop when playing to remove himself to go potty either. I have tried all kinds of bribes so has daycare.
My freakin question would be htc you potty trained for home in the first place. Ive tried everything on google and took advice from others. My daughter just wont go. Not only does she have issues pulling her pants off but even naked she doesnt run to the potty until after shes already gone. Ive tried being naked, her going to the potty with me, training, panties, regular panties, etc lol