I do not get it how an antibiotic cannot destroy a periodontal abscess and dry it up. that is what it is made for, right dentist?

Antibiotics & Teeth: Antibiotics control and manage infections until the cause of the infection can be treated. For example, an infected nerve in a tooth needs to be physically treated.. antibiotics cannot replace root canal therapy. In the same way, your periodontal pocket needs to be treated... antibiotics cannot replace periodontal care. The abscess returns again and again without definitive care... got it now?

See an Oral Surgeon: Oral antibiotics do not help resolve the cause of the infection. If the gum boil is chronic and does not resolve then removal of the impacted tooth (cause) will be necessary. See an Oral Surgeon for evaluation and definitive treatment.