I checked both medications with a drug interaction checker and no interactions were found for your medications (Levethyroxine and Clindamycin), although it is always best to ask your Pharmacy also. If you are taking any antibiotic, the are designed to kill bacteria, In the stomache, you have good as well as bad bacteria, this good bacteria gets killed also, so to avoid digestive issues, you should take a good Probiotic, You can find probiotics at most health food stores, Jarrow has a good product high in count and non dairy, or if you enjoy yogurt, you can eat three or four of those small cups per day, this keeps the good bacteria in place. Best Wishes FTB4
I just finished a course of clindamycin for a tooth infection, and as FTB4 said, it does not interact with levo. Listen to his advice about the probiotic and/or yogurt. Clindamycin messed up my gut worse than any antibiotic I've ever taken (which isn't many).
Also, is your sore throat and runny nose due to a bacterial infection? If it's due to a cold or the flu, both viruses, no antibiotic will help it. Antibiotics kill bacteria, not viruses. Misuse of antibiotics for viral infections has contributed to drug resistant strains increasing. So, check with your doctor first to see what you're dealing with.