Your baby is still very young (<4 months). There is a theory that the first 3 months out of the womb are like a 4th trimester of pregnancy. Your baby still needs a lot of sleep, and may want the comforting rhythm, movement, and sounds of your body. There is a lot of pressure in Western countries to wean children off this dependency on the mother for sleep. This is not natural in the first three months, nor is it necessary even beyond that, until this “dependency” becomes a problem for you.
You could try to find ways to help your baby to sleep while meeting some of your own goals, such as working on your phone or laptop while feeding or hugging, or enjoying a walk, podcast, or audiobook with your child in a carrier. Call on your friends and family to hug or carry your baby while you catch up on some much needed sleep.
By helping your child to settle, you are still teaching some of the important skills needed for self-settling.
Evidence is mixed as to whether increased carrying decreases colic. One random controlled trial found increasing supplemental carrying (more than just when baby is crying) produced a 43% decrease in crying (Hunziker and Barr 1985), another found minimal effect of carrying beyond being responsive (Barr et al 1991).
Please add your experiences with this approach in the comments below.