Breastfeeding is healthier and absolutely worth it, but don't be ashamed if you need to resort to a little formula sometimes. There's a weird, toxic culture that's grown in recent years where women are shamed if they formula feed, even if it's just as a supplement.
We've given birth at hospitals in 3 difference states, and in each one there was an uncomfortable tension between the lactation consultants and the doctors/nurses, who would often given conflicting advice. It took a couple of weeks for our first baby to learn how to nurse because he was in the NICU, so he had formula. The other two picked it up quickly, but we still supplemented with a little formula in the hospital the first couple of days because they lost too much weight (10%+) and were dehydrated.
Most of the lactation consultants we encountered were often scoldy, pushy and dismissive, and would treat my wife as a failure for allowing her kid to drink formula (even when the doctor strongly recommended it). It was really weird.