I use Loestrin Birth control. Recently, I got the Flu and started to take Mucinex DM daily. On the second week of my pills for the month, I started my period. Is my Birth Control Working? Or, Did the Mucinex DM mess up my Birth control. Is it safe to have sex without fear of getting pregnant?

I am sure you realize that no birth control is 100 percent, so it is never safe to have sex without some fear of pregnancy.
It is of course a small chance, one in 1000 perhaps, but still a chance.

Did you just start the birth control pills ? But yes medication can weaken the effects. So yes the birth control should still be working, but the effects may not be as strong

It says on the instructions that certain antibiotics and other meds will weaken or even disable the protection completely. It is not safe to have sex without fear of getting pregnant until you have been off the other meds for at least a month. Just use a condom until then!