I've been using saline drops & suction bulb for my 3 month olds stuffy nose but now he has a wet cough. Can I also use the suction bulb for his mouth?

Yes. Saline & suction are a good standby for simple nasal & oral airway maintainance. There is no reason not to use a nasal aspiratorr in the mouth, they are connected surfaces. As long as baby is feeding well & playful for most of the day this is a fine approach. If you notice baby working harder to breathe, dropping feed volume or appearing restless or tired an evaluation may be warrented.
Suction bulb. No. It is time to call your doctor for an appointment to examine your baby to find out the cause of the congestion and cough. There are several possibilities.