Awww...poor rattie! I have never given my rats amoxicillin, but I have given them Baytril for a case of pnemounia. It is also a good idea to keep them seperated, and wash your hands after handling the sick rattie.

As Wolfsoul said, it is quite possible that they could be from the same litter.

I hope your rat gets better soon! Have a safe trip to the vet!