I would see if TSC has Penicillin. If they have long acting Penicillin, that is even better. If it is Procaine G then it is just the regular stuff. I can't remember off the top of my head what the name of the long acting is. I don't know what goat dosages are but for alpacas it is 3cc per 100 pounds. I bet goats are pretty close to that.
I would also dip her navel again and really soak the area. I keep film containers and use that on navels.
If you have some Banamine, I would get that into her too. But take her temp first and see if she has a temp.
I would at least dip her navel again and then go from there. You hate doing things too quickly but you hate waiting. I have seen too many crias go downhill fast so I usually move pretty quickly with babies.
If you get long acting penicillin, the dosage for alpacas is 4cc per 100 lbs. I would weigh your little one and use the alpaca dosage. Also get 18 needles since the Penicillin is thick.
Second, you worry like I do!!! My 2 kids, although not birthed here, have snotty noses and I'm at a loss with what to do. I do not have TSC, and my farm stores don't seem to have a huge selection of "stuff". I definitely feel for you!
Sounds like Ginger is a great mom, and I'm sure Peach will be fine