It depends on on how badly your molar has been affected by the infection. Your infection may have healed itself by amoxycillin. If indeed the infection has been completely cured by the antibiotic then you will get no more pain. Then again if your molar has already been seriously weakened then it will slowly break down over time and that may cause pain again.
A root canal actually will stop the pain from recurring. With root canal your molar will still slowly break down over time but you will not feel any pain. The cap is required to make sure it does not break any further.
Whether indeed cap is required or not that is debatable. I had a similar problem 2 years ago and my dentist told me I needed a root canal and cap as well. He told me my tooth would easily break down if I did not put the cap on because it had seriously weakened. I, however, only went for the root canal. It's been 2 years and surprisingly my broken tooth hasn't broken any further at all. I eat all sorts of hard food with that broken tooth with almost no problem at all even though I did not put the cap on.
Finally, it depends on the condition of your tooth whether you require a cap or not. If your tooth is moving a lot but not causing any pain you may even choose to skip the root canal as well.