Well, I'm no expert, so let's start there, but it is obvious to me that your baby isn't getting enough sleep. The reason you're having such a hard time getting him to sleep is because he is overtired. I would try to get him on the EASY schedule (Eat, Activity, Sleep, You time, from the Baby Whisperer). In other words, he eats when he wakes up, has a period of activity and then sleeps for awhile so that you have some time to yourself (even if it's only 30 minutes). Then, when he wakes up, the cycle starts again. This age is tough because they are starting to realize when you aren't around. Also, you really are going to have to sleep train him if you don't want bad habits to form. Nobody says you have to leave him crying for 30 minutes until he throws up, but my son had to cry for a few minutes (sometimes 15 or so) for a long time before he learned to put himself to sleep on his own. I just went in to check on him every 10 minutes or so and would give his paci back or soothe him for a minute and then try again. In the beginning, sometimes it would work after one or two tries and sometimes I just had to get him out of his crib and hold him because he would be too upset to calm himself. It takes time, but I don't know of any way to get a baby to just start falling asleep on their own with no crying. I think there is a book called the "No Cry Sleep Solution"....I have seen posts about it on this site, but I haven't read it, so I have no idea how it works. Maybe check that out from the library and see what it has to say?
I have 2 kiddos and honestly, sleep training was the toughest part of parenting a baby that age, but I am so glad that I did it because my 3.5 year old sleeps in a big girl bed (since the day she turned 2 years old) and has never gotten out of bed once we tuck her in at night. She will lay there and listen to music and talk to herself or her stuffed animals, but she never leaves the bed or the room. She is comfortable there and knows how to put herself to sleep (and has since she was 4-5 months old). My son, who just turned one a couple of weeks ago also puts himself to sleep with no crying now. It took longer for him and he probably didn't stop the fussing until he was around 8-9 months old, but the crying times got shorter and shorter and fewer and farther between. This is an important skill and the earlier they learn it, the easier it will be. You don't want to be on Nanny 911 2 years from now because your toddler won't stay in his bed.
If he is feeling better and the congestion has subsided a little, then I would really work on getting him in his bed. At 5 months, he is becoming VERY aware of the difference between the crib and the swing and will have an obvious preference. Again, a habit can form very easily that would be hard to break later. Can you raise the end of the crib so that he is not laying flat? That might help him breathe a little better when he's sleeping.
I know this probably wasn't much help to you because you didn't want advice on crying it out, but I really think if you work with him and help him learn to do this, you will be successful and you won't have to hold him or rock him to sleep. He really can learn to do it on his own, he just needs some help. The other thing that I invested in that I LOVE is the Fisher Price Aquarium for the inside of the crib. It has music and lights and bubbles (there are different settings, so you can have just music or all of it) and both of my kids loved that. They even learned to push the button themselves to turn it on when they were a little older. I think the new models even come with a remote control so you can turn it on from outside the room. This might also help soothe him. Try to get a routine going for him and do the same thing every time he goes down to sleep. I know this is very long, so I'll stop rambling. I just feel for you because I know how frustrating this can be (my son was a VERY difficult baby and had reflux on top of it, so we had a harder time getting him to sleep well also). Just remember, sleep begets sleep, so the more you can get him to rest, the better he will sleep once he's down. Good luck! Sorry again for the long post.