as long as there's no fever or he's not making a "Whoop" sound or weez when he coughs, you should be ok until his upcoming appointment for well-baby check. But ALWAYS call your doctor to be on the safe-side of things. Don't ever hesitate to phone them with a concern.
Your sister is right- buy some saline (salt water saline) and for the initial snot-removal, put 2-3 drops of it in each nostral and let it set for about 5-10 minutes, in the meantime, set up camp with a syringe, a paper towel and a wet wipe (to wipe his nose after you're done). Cradle him in the nuk of your arm and you just have to syringe as much as possible. He's going to scream and cry, yes, but don't let that stop you. The more you get out and faster you do it, the better he's going to feel cuz it's also more than likely the cause of the coughing too from when it drains down into his throat. After you clear it all out, just through out the day like once in the morning and once in the evening, put a drop in each nostral to keep it moist and from letting it get too congested and don't worry about syringing again unless he's startn up again where he's snorting, gagging, etc.. I've had to do this for my son since he was 4 weeks and had to really be religious about it for aprx. a week strait. It's that seasonal change of the year, so the youngins are going to get congested. It sounds normal to me. Hell, as I'm typing this, I'm listening to my little guy in his moses basket snoring away. LOL.