Anyone else’s lo not go pee in the public potties?

My 3 year old daughter says she’s scared. She has never had any incidents that I know of to make her so scared so idk. She goes just fine at home in the big potty. But anytime we are out of the house/running errands I have to take a mini potty everywhere we go. Also, she started her daycare about a month ago and has yet to go on the potty there. She usually waits until nap time and goes pee in her pull up. 😔 Today was her first accident at school. The teacher even told me she offered her chocolate and she still wouldn’t go. I’m thinking I’ll try to encourage her to go on the daycare potty every time I drop her off/pick her up and hopefully that’ll build her confidence, but it just sucks that she holds in her pee. I don’t want her getting a uti from it!! Any suggestions on how to build her confidence would be great!