Is it safe to use chlorhexidine gluconate mouth rinse for infected gums over wisdom tooth?

Yes: Chlorhexadine oral rinse is an excellent and very commonly prescribed anti microbial mouth rinse. In the short term, in can help lessen the acute phase of infected tissue around a wisdom tooth. By no means will it solve a problem other than some short term relief. Have the wisdom teeth removed.

Yes: Can not hurt and might help.

Safe, yes. Effective, not so much. Mouthwash is NOT a substitute for proper oral hygiene. At your age flossing daily is even more important than brushing 2x/day w soft t'brush for 2 full minutes by the clock.