Six month old still doesn’t sleep through the night

We need to do sleep training already for our baby. She’s never slept through the night. I put her down around 6:30 and she wakes up at least once between 6:30 and midnight usually around 10 /10:30 or midnight. We feed her then. (Formula fed). Then last night she got up at 3:30 and then at 6am was up for the day. She doesn’t sleep well and neither do my husband or I but I worry more about her bc I want her to learn how to put herself back to sleep. We still rock her and I know we are not helping her by doing that. Our pediatrician yesterday said at her six month appt. that most babies at this age don’t need to eat during the night. So do we not feed her anymore? She also gets stuck in her crib bc she corners herself and then cries. The other day she wet herself so I changed her. I really want to start sleep training and I think we will start today but I’m also worried about it bc I hate the idea of her thinking we are not responding to her needs. Can anyone tell me what worked for you with your little one?? She really wants to put herself back to sleep but can’t she needs us to rock her and it takes sometimes up to an hour. It sucks. ☹️