Oh poor Olivia! :sad3:
Are you sure she's peeing the blood and it's not coming from her vagina? Is she spayed? If not, you might consider it could be vaginal bleeding. Of course, this isn't good and a spay would be honestly be the best thing (unless she's elderly and you need to judge her health by her age etc).
We had a similar experience and it actually took me a little while to see who it was too. Females are very good at cleaning themselves. What I did was pick up the girls while they were sleeping and before they could get cleaning themselves. Sure enough, Venus had blood around her vagina.
Our vet put them on Baytril and within a couple days, the bleeding stopped. But considering the bleeding is probably a symptom of a larger uterine problem (tumor, cysts, pyometra etc), we had Venus spayed. She lived another year and a half, to a ripe old age of 38 months.
Baytril is definitely a better choice than Doxy and more "well rounded" in case like this, where you aren't sure. Cefa is another good choice (much like Convenia) too.
Do keep us posed on dear little Olivia.