When they are windy, as it hurts so much they find it very comforting to be close to you. Also being upright can help the wind come up. Sorry I am stating the obvious here.
Generally speaking I rolled with it with my two until about 4 months after any wind issues had long gone and then I did a gentle bit of sleep training using the Baby Whisperer pick up put down method.
Keep them awake for no more than 2 hours at this stage and watch for sleep signs i.e. decreased activity, slower motions, less vocal, quieter, calmer, eye lids drooping, yawning, eyes less focused, appears disinetrested in surroundings etc. AND then start the soothing to sleep.
Two hours of wakefulness is about the maximum a baby can endure without becoming overtired. Sometimes babies may need to go to sleep after only being awake for an hour, this usually occurs first thing in the morning. Try to soothe them to sleep before they become overtired. It's OK to soothe to sleep at this age, they're so little, you won't teach them bad habits, BF/ or bottle feed to sleep in a darkened room in the quiet, rocking, swaddling etc. And then gently laying down in the cot should be fine. Putting an item in the cot that smells of you can help too.
You could look into buying a different sling that is better for your back in the meantime? Or Co-sleep for daytime naps, let them fall asleep on you and you can have a nap too. Let the chores wait. Enjoy your baby, they grow so quickly.
Have you tried swaddling? In the early days with mine I would soothe to sleep on me, swaddled in a dark room and lay down once they were in a deep sleep.
It took with my second baby who was very windy up to 10 weeks to settle easier. Even at feeds at night he'd squirm with wind after and be uncomfortable for ages. My usual blurb I give out is basically to try not to worry. It's such early days; you cannot spoil a baby at this age. Do whatever it takes to survive
Soothe to sleep on you and roll with it my lovely. They'll settle down again soon enough.
My second child cried for 2 to 3 hours a night until aged 10 weeks and I spoke to my health visitor about it, she agreed it was probably colic and her tips to try were:
Warm bath covering tummy.
Lying him on his tummy with a warm (not hot) hot water bottle under him to soothe tummy.
Cycling his legs whilst he's on his back. Holding feet palm to palm and rocking legs sideways, whilst lying on floor or lap.
Or scooping with right hand down his right side whilst holding feet palm to palm.
Or rocking him face down well supported on legs.
She also said don't eat anything that gives you wind such as brocolli, cabbage, caffeine, cauliflower, garlic or other stimulants if BF. She said if none of the above did work I could try buying Colief drops from a chemist and mixing in with feed by expressing it first, as she said sometimes colic is caused by a lactose intolerance.
I found that out of all of those the cycling the legs was particularly good. I also found that as he had trouble burping, the infacol made him cry harder as it coalesced the bubbles into one big one that still went downwards but hurt more. But giving him gripe water after every feed straight away really soothed his tummy. I had to do it every feed though without fail.
The warm bath in quiet room was also a real help. Every night at the time he started to get agitated I would put in the bath, in a bath cradle and keep putting warm water on his tummy and every now and then top the bath up with warm water, so it wouldn't get too cold for him. Once or twice he was in the bath for 2 hours in the early days as it was really calming for him. Once he started doing big yawns and it was bedtime, I'd take him out into a dark bedroom and change him and BF him quietly and then often he'd go to sleep straight away. He'd wake for feeds at 10.30pm, 2am and 5 am often at this stage.
Remember things will get better soon lovely, sending you a hug x
I suspect I may have repeated myself here, as I need to dash off but wanted to send you my tips, for what its worth.