Additionally, the active ingredient in Mucinex is guaifenesin (GU). GU is an expectorant, meaning that it loosens mucus in the lungs to give you a more productive cough. What you would want for night would be a cough suppressant.
You are doing all that you can right now. It will just take time.
ETA: I wanted to address what Sandy has said about parental dosage mistakes. It is very true that these recalls we've all read/heard about have to do with mistakes made in the amount of medication given to a child. HOWEVER, many infants are unable to metabolize some of these active ingredients and when they are given subsequent doses (even when directions are followed properly) they are inadvertently overdosed and could possibly die as a result. At 6 months, a baby's system (no matter their weight) just isn't developed enough to handle these medications.