Perhaps the pill is chlorpromazine which is an antihistamine. This really wouldn't help Little Bit because her problem is not an allergy.
If you can keep her nose as clean as possible, this will help her to breathe more easily. Saline drops in her nose may help. . .it wouldn't hurt her, but I doubt she will tolerate this.
Since this upper respiratory infection is mostly if not all viral in origin, antibiotics don't completely treat this and therefore there is not a quick response. It's like colds for us, we just have to live through them.
If Little Bit is not eating well, warm up her food to make it more fragrant. She's more likely to be able to smell it then and eat. If you don't feed her canned food, she may prefer this right now. Also, meat baby food warmed up is sometimes well liked. You'll have to offer her fresh food 3 or more times per day.
Keep her nose and eyes as clean as possible.
Sometimes cats won't drink like they need to during an upper respiratory infection. In this case you'll have to see your vet there for some subcutaneous fluids. Usually, this is not necessary, but just in case.
Little Bit should be fine in about 1 week.
Best of luck to you both,