I have strep throat, went to the er and got the penicillin vaccine. i've been coughing up infection and it's coming out of my sinus'?

Need more antibiotic: possibly. I am guessing they gave you an injection of Penicillin antibiotics. Did they give you a written Rx for more antibiotics when you were discharged? If not or you feel like your symptoms are not improving, you need to see your PCP or urgent care for them to re-evaluate you and determine if you need a course of oral antibiotics for ongoing infection as it sounds like this is the case.