Cefdinir 600MG and probiotic sinuses draining into throat, cough up white foamy/slimy green mucus. When I swallow after, hear/feel crackle in throat.

Take full course. I'd keep going with the cefdinir it until it's all finished. I am not sure how long you've been taking it but if you are on days 1-7, have faith and keep going. If you have any new fever, or are having additional symptoms after one week on meds, that would be time to return to your doc for re-evaluation. You're on a potent antibiotic, so I bet you'll be feeling better soon. Rest and fluids!!