please help with your advise....

Hubby has had latent problems related to 2 teeth for quite a while now. The problems seem to "subside" and he can go for relatively long periods with no pain or indication that there´s something "simmering". The last time at the dentists they found holes (carries??) in both of the problem teeth (each are on different sides) and the dentist wanted to take it out because the teeth are so-called "jacket crowns" and each one is a part of a 4 tooth bridge..... complicated???!!!
Because of the complication and expense involved he´s been treating the problem (unfortunatelñy only recently) with natural means (homepathy, oil gargling and started brushing with a mixture of sodium bicarbonat and a good Sea Salt ) and up until now has had no serious problems.
On his latest dental visit for cleaning they remarked how much the gums have improved and the tooth-staining was greatly reduced compared to a year and more ago.
He decided to ask the dentist, if she thought an Antibiotic would also help to keep the peace until we had the possibility and $$s for a lasting solution. She´s recommended Clamoxyl (GlaxoSmithKline - which is Amoxicilina ). He promptly bought it and before taking, I thought of asking here for a better solution. To make matters worse there´s not only Aspartame E951) in it as well, but the "prospect" says it could cause problems with liver and kidneys... did´nt mention of course the damage the Aspartame would do. This solution had also been recommended by many so-called dentists on the internet and hubby asked the dentist if she thought this would be feasable.
Pl help - 1) if you know of a better way to solve this problem
and 2) if you know of any major side-effects of Amoxicilina so he could (in an acute emergency) take another antibiotic.
Appreciate all help and thank you for reading this long "story".