B.M.
Sounds like she's doing fine. No fever. Two days into a cold, you can tell how bad it's going to be usually. If he just has a runny nose, consider yourself lucky.
That being said, nasal congestion can be tricky for a nursing baby, because you can't really nurse when you can't breathe through your nose, and you get frustrated and cry a lot, all night long.
When my son was very small, not as small as yours, maybe 2 or 3 months, he got a bad cold, and I learned a few things. Nurse more than usual- if he cries, nurse him, if he opens his mouth, stick a boob in it. They need the comfort and the fluids. My son woke in the night miserable and congested, crying because he couldn't nurse. I took him in the bathroom and ran a hot shower and just sat in the room holding him. It helped his congestion and he nursed himself to sleep.
Another very primitive solution- I'm warning you, it's kind of gross- is to just forgo those nasal aspirating bulbs and do it the old fashioned way. Do you see where I'm going with this? Once or twice when my son was sick with his first cold, and it was the middle of the night and I was desperate, I just put his little nose in my mouth and sucked the yuckies out of it. I couldn't believe I did that, I just did it by instinct without thinking twice. It worked. And it wasn't even as gross as you would think. It's a tiny ammount of baby boogers. It's not like being on Fear Factor.
Anyway, good luck. Try to relax. It's going to be okay.