My tooth pasta is damaged and it caused gum infection. right now my gum is swollen. can i take amoxicillin 500mg to treat gum infection before i repair my damaged tooth pasta? if yes, is it every 12hrs?

Have no idea what "tooth pasta" means. Also, antibiotics alone will not cure gum disease. You need the services of a Dentist, preferably a gum/bone specialist, a Periodontist. Self diagnosis/treatment can be at best ineffective, at worst dangerous.

An infection from a broken down tooth should be evaluated by your dentist before antibiotics are taken. Needless use of antibiotics can cause resistance.