My son has been sick with one thing after another since he was born. He's now almost 9 months old and is currently sick with RSV and a secondary ear infection so do I know about trying to get a sick baby to sleep!
First try elevating one side of his crib about 3 or 4 inches, this will help with his sinuses draining. They make wedges that you can buy but a rolled up towl will work too. Also, Vics makes an infant chest rub we use every night. Smells more pleasant than the adults version and is much more gentle. Putting a humidfier in his room will help a LOT. It keeps the snot thinner so his body can rid him of it. Without humidity, the mucas gets thicker, harder to get rid of and just hurts more in the nose and throat.
Infants need sleep to heal so make sure he gets his naps but before bed give him is last meal and make it a big one. Give him a nice warm bath and using the wash that has the vapo-rub in it will help too. Rock him and give him a little Tylenol or Motrin if you know he's got a sore throat or something else that hurts. Run the humidifier all day and night so the room is nice and moist and get him tucked in.
I've made the mistake of relying on the swing for our son to sleep in. Do NOT do this. I actually just posted a question the other day about getting him out of the swing and into bed more. If you haven't started this habit already then do yourself the favor and don't.
But all the little things really add up for a baby who isn't feeling well. We like to be pampered when we're not feeling well, it's the same thing. If he's not feeling well, make the evening before bed extra special...a nice long warm bath, a massage with some lotion and some Vics rub on his chest...it's about all you can do for him.
Hope you find some help in this. Best of luck. Being worn out from a lack of sleep is something I'm too familiar to.