You might refrain from filling the sink with hot water. I'm not sure that would help anyway...and if there's any chance they could get up there...well, you know. :weepy:
It really works best, if the doors are shut and you are in there with her, while the shower is running. yeah, you get kinda sweaty. But just hang out with her on the counter, while the room gets steamy. Unless the other girl isn't feeling well too, you can probably leave her back in the cage, so you can focus all yoru energy on Lola.
Baytril and Doxy really are the best antibiotics to treat URI in rats. Chloramphenicol is known to be another...but is stronger, and in my opinion, not needed for the first flare up (plus, my guys hate it and it has been known to give a few of them, the runs...NOT fun). Zithromax might work too...but it's considered one of the big guns too, and not generally used as a first line of defense. If you think you might want to take this info to the vet (coming from just a rat owner, who has learned directly from her exotic vet). The dosages for rats are 5mg/kg for the doxy and 5-10mg/kg (depending on the severity of the URI) of Baytril. If your vet gives you one or the other, that's great! Both are very bitter, so if there's anyway you can have the meds compounded into something yummy, great. Otherwise you'll need to find something you can "hide" the meds in. A dab of Cool Whip works great for my gang.
Some non-exotic vets will try and tell you to put the meds in their water. BAD IDEA! There's no way to make sure they get the doses they need, and the bitter taste makes them not want to drink water. So it's bad all the way around.
I would definitely try and make sure you get enough for 2-3 weeks at the VERY least. if you are only give a 7 day dose, odds are, she's just going to fall ill again, after you take her off.
Something you might want to consider getting (though you probably don't have time to get it and take it to your vet) is the Rat Health Care Guide. It has a lot of useful info for rat owners, and some med info too. Before I found my exotic vet, I took the RHC guide to my regular vet in hopes it might help.
As for foods our ratties like: Frozen (thawed) corn, peas, cooked pasta, cooked sweet potato (no skins), canned cooked kidney or black beans, baby carrots, blueberries, grapes, watermelon, cantalope, (I usually give just one kind of fruit a day), broccoli, kale, cilantro, cooked rice, the occasional scrambled egg, soy yogurt, oat milk, soy milk, even some cooked chicken or turkey. We don't give our rats lettuce, as it doesn't have enough nutrional value for them. I'd stay away from salty things like chips and crackers. But I've been known to share my left over blueberry pancakes, cheese omlett, mac-n-cheese with them. As for treats, we buy the honey flavored animal cookies that you can get in the bulk food section of the store.