Peeing anywhere but the litter box is very good indication of UTI. Antibotics for 10 day will take care of that problem. Must see vet.
Ignoring it is hazzardous to kittys health.

Halo will get used to carrier. Maybe try putting her in carrier at home every so often so she doesn't associate all the time carriers mean going to vet. Also, put treats in carrier and favorite toy.

Our kids go into carriers when there are tornado warnings and we all head down to basement. Butterscotch loves being in carrier to watch when we have work done on the inside of house. Thumper and Skinny perfer the bedrooms. Butterscotch is Mr. Nosey

Make carriers a postive experience.