Try a product called gripe water...it works very well with gas problems, many moms on here (including me) give it a thumbs up. Also, it's true that nursed babies need to be burped less. I rarely burped mine when I nursed. THey aren't taking in a ton of air when they nurse as compared to a bottle. The reason for his tummy issues may be what you are eating, not the lack of burping.
I'm also like lex jude...If DD doesn't burp after a minute or so I let it go
Also, for gas, lay him down on his back and gentily pump his little legs. Push his knees up to his chest and them stretch them back down. That helps get the gas moving and moving out! Do it kinda slowly.
Good luck. If he keeps having a lot of problems with gas that is really bugging him, talk to the doc...you may need to change your diet or try a soy or lactose free formula. Congrats on your new little angel!!