OK, first of all, don't give a 5-week old water!!! Whether you are breastfeeding or formula feeding, no child should get anything else to drink until after 6 months. She is getting the fluids she needs. The AAP is pretty clear on this, I don't know why doctors recommend things against their governing board:(
So, that aside, it sounds like you are doing what you can. If you think that maybe her throat is sore from the coughing, you can give her a small dose of infant tylonal. If she doesn't seem affected, I wouldn't worry too much. It can be icky to continually be cleaning her nose (especially if you ARE breastfeeding and she gets snot all over you every time - I know how that goes...ick...) A humidifier in her room will help a lot (or your room if she's sleeping with you...it will help you too!) If you want to keep track of how humid it is, you can get in expensive thermometers that will tell you the humidity. Usually you want to keep your house around 68-70 degrees and 40-50% humid, but if she's still having trouble, you could try to bump that up a little, especially in her room.
If you are breastfeeding, it will help keep her ears clear. Also, if you pump a small amount of milk and use an eye dropper to drip it into her nose, it's better than saline! I know it sounds gross, but breast milk is anti-fungal, anti-bacterial, and sterile. Put a few stops in each nostril and wait a couple minutes, then use the nose bulb from the hospital to suck out what you can.
If her nose is red and sore from the salty snot and rubbing tissues, I use my purelan on my son's nose and it helps a lot. It both soothes and creates a barrier so the snot doesn't irritate as much.
I hope that's helpful. Keep your hands clean and give her lots of love, she'll get over it:)