Feels like something stuck on side of throat and painful if I touch/swallow/. Post wisdom tooth extractions. (See last question) Can it be abcess?

It is possible. but it's all normal after wisdom tooth removal especially if the surgery was complicated. Many patients complain of difficulty swallowing after surgery. Swallowing can be improved by using NSAIDs, mouth gargles with warm salty water the day following surgery and if concerned see your surgeon for a check up.