It is not your fault!!!!! Your son, like my daughter is not a good sleeper. My daughter never was. She is 16 months old, and still wakes up once. I give her water. Your son still needs formula. I rememeber when my daughter was 7 months old very well, as I journaled everyday about her. I still journal everyday. Here are some questions. Is he on solids(stage 1 foods)? How many oz of formula is he drinking and how far apart? When time do you put him to bed? What is your currant routine? Now, Here are some suggestions: Do not feed him everytime he wakes up. It may make him feel uncomfortable and bloated.
One hour before bed feed him a veggie. Then right before he is to go to bed, fedd him a 6 oz bottle. Make sure he burps good. Then off to bed he goes. Then the next time he awakes(Hopefully not for like 5 hrs) just go and soothe him. See if that works first before resorting to the bottle. If it doesnt then feed him 6oz, burp, and put him back in the crib. If he wakes up every 3 hrs, he shouldnt need a bottle every time.
Do not let him scream. He may cry it out a bit at his age, but the screaming he cant.
Just be patient!!!!!