9 month old - trapped wind

Hello,
My 9 month old baby has had digestive issues from the beginning. She has a hard time burping and passing gas. After feedings I have to burp had at different spots for at least 40 minutes to get the gas out. Putting her on her belly or letting her crawl does not help. Most gas is on her lower left side and upper left side close to arm pits. I have to burp these areas constantly to get the gas out. She has had this issue when she was on 100% beastmilk, 50-50 breastmilk and formula and now on 100% formula. Sometimes when burping does not help, we give her gripe water and then burp her and that helps her release it in a big burp.
She typically rubs her eyes and puts her fingers in her mouth when she has wind.
Diet - 3 meals a day and 4 bottles of formula a day
Bowel movement - Her bowel movement is good as long as she drinks her milk and water. She has 2-3 per day.
Allergies - She is sensitive to milk protein casein and gets eczema and increased gas if I give her a casein based formula or if I consume casein. She tolerates whey and lactose ok.
Temperament - She is a happy baby. She is sensitive to loud sounds and starts crying with vacuum or food processor. Loud sounds also tend to wake her up - very light sleeper.
Sleeping pattern - she is a good sleeper as long as she has been burped completely. Takes 2 naps a day and sleeps through the night. At night she wakes up crying 2-3 times but can usually put herself back to sleep. If she does not, I give her water and that helps.