Rat Breathing Heavily

What does her breathing sound like? If it's a URI you do need to act quickly. One of my rats had a URI a few months ago, and we ended up bringing her to the emergency clinic because we were so worried. She seemed fine in the morning, but by the time we left to take her we were afraid she wouldn't make it through the night. It progressed pretty rapidly. Granted, she's fairly old - she'll be 4 soon - so rate of progression might be a bit different. Regardless, URIs can progress quickly, so I would highly suggest taking her to see a vet ASAP.

Her breathing isn't noisy, but she does do a quiet sneezing sound every once in a while but not very often. I will try to take her to the vet asap, but I can't until after school tomorrow. Can I do anything in the meantime?

You can use a humidifier or steam her in a bathroom.

In my experience "quiet" infections are usually Lower RIs, which are more dangerous and can be fatal.

Relatively how much time do you think I have? It hasn't worsened in the past day.

The earlier you can treat the better. If this is something like abscesses in the lungs, you'll need to start treatment fast. With something like pneumonia, which this could be, I wouldn't wait longer than a week from symptom onset.