Hi there! What a gorgeous kitty! I thought she was all gray on a quick look, but now I see she may be a tortie?
I'm glad that you went ahead and made the vet appointment. Is she using the box frequently but not producing big pee clumps? It sounds like she may have a urinary tract issue - maybe an infection, or crystals. Peeing frequently but in small amounts, frequent licking of the genital area, and peeing out of the box are pretty common symptoms. The not-using-the-box thing is often because it's painful to pee, so kitties associate the litterbox with pain.
In the meantime, make sure to clean the areas where she peed very thoroughly with a cleaner specifically formulated to get rid of kitty pee, like Fizzion or Nature's Miracle. Otherwise, even if you smell absolutely nothing, your kitty will still be able to smell it, and that will encourage her to keep peeing in those same places. With NM, you really need to saturate the rugs thoroughly, so that the back is completely wet also. I'd also spray some on the floor underneath and wipe that up. For sheets, I believe NM makes a laundry additive. I'm not sure it's necessary - I've never used it - but just something to keep in mind. Once the rugs have dried (you'll smell kitty pee until they're completely dry), you could cover them with plastic until you're sure that she's using her box regularly again. I have my guest bed covered with the plastic bags from the dry cleaner. Not very attractive, but preferable to another ruined comforter!