Breastfeeding to sleep

Anyone that used to breastfeed their baby to sleep? Do they grow out of it or do you defo have to sleep train. My midwife mentioned sleep training my daughter (3months old). Doing the pick up and put down method, but I can’t stand hearing her cry so hard. She’s also teething so it’s breaking my heart. I just need someone else’s point of view. She’s also not feeding well because of the teething so the only time she feeds is when I feed her to sleep while she also uses me as a teether because she can’t pick up and put things to her mouth yet x