Hello and hope you are doing well.
The receding painful gums and the blister may not be related to the throat infection. They can occur due to local or systemic causes. Local causes like tooth infections, tooth abscess or periodontal disease. Some medications like dilantin and calcium channel blockers like nifedipine can cause swollen and painful gums. They are more common in smokers, in people with poor dental hygiene, with vitamin deficiencies and are known to be associated with stress. The blister could be canker sore or it could be due to STD. It is difficult to tell without examining what exactly is the cause for your symptoms.
So continue with the antibiotics, as this may help with the oral infections also. If they still persist after the course is over, consult a dentist.
Hope this helped and do keep us posted.