Can long term antibiotic use cause abdominal swelling and if so, why?

Yes: Candida infection, and rarely if cause drug- induced hepatitis.

bacterial imbalance: There can be many problems assoc with prolonged abx use. The abx will sometimes kill off the "the good bacteria" that helps us with digestion and results in the overgrowth of other organisms (bacteria and fungi-yeast) witch can effect us adversly. The goal is to take abx only if absolutely neccessary and for short periods , the use of prebiotics and probiotics has been shown to be of benifit.