OK, I'll try.
Your baby's rash is not an allergy to amoxicillin because, as you point out, the rash preceded it. She is also not allergic to neurontin, because the rash would not have gotten much better while you are still taking it. (Allergies to drugs in breast milk can in theory occur, but they must be awfully uncommon; I've never seen one.)
By a process of elimination, then, your baby's rash appears to be something other than a drug eruption. What could it be? While I obviously cannot say with certainty, the most common itchy rash in infants is eczema. This would get better with cortisone creams, and would be likely to reappear a little off and on thereafter, just as you say hers does.
Can eczema come all over "out of the blue?" You bet--happens all the time. Cause? None--that is, the sensitivity involved is hereditary, not allergic or environmental.
My advice is therefore the following:
1) Have you doctor examined by a dermatologist, who can give you a definitive diagnosis.
2) Continue the neurontin, if your doctor feels it's best for you, without guilt. In all likelihood, you and your needed treatment are not responsible for her rash (which may well get milder as she gets a bit older.)
Best.
Dr. Rockoff
www.valleyfever.com
http://www.csubak.edu/healthcenter/ValleyFever.htm
http://www.casa.arizona.edu/~peter/valleyfever/web/page4.html
Thanks for listening,
gydget