Thank you for the update, and THANK YOU for giving her a box inside.

I doubt she was "protesting". Cats don't think like that. It's more likely she finds it very difficult and uncomfortable to use the other litter box.

Cats can't talk, so when something is wrong they have to find another way to communicate to us that something is not right in their world. Inappropriate peeing is the most common way they tell us.

Blood work will not diagnose a UTI. The vet needs to take a urine sample and test it. But I am glad to hear she is using the box in the house.