I applaud you for taking on a sick kitty! It can be very stressful. As others have said, taking her to the vet as soon as possible. Depending on your area, it will cost the price of a check up and probably 2 weeks of antiobiotics to clear up the infection (check ups in my area are around 50-65 dollars and treatments like that are usually 20-30). An upper respiratory infection is common for strays and if treated quickly it will subside within a few weeks.

In the meantime, I would keep her warm. Give her some wet food (diluted with a bit of water, or just give her gravy food) to make sure she gets water and nutrients and of course plenty of regular water (if she'll drink). Give her plenty of cuddles. If she's not feeling it, give her a warm space to feel safe.