4 month old going for no sleep

Help a girl out please! I am a first time mom and need some advice. My four month old is waking every two hours overnight. I first always try putting her back to sleep with just touching her, it never works, so then will pick her up and rock her back to drowsy and lay her back but long story short no matter what I do for how long I end up feeding her and right back down she goes then. Even if she is awake, once she eats I can lay her back down and she will work herself back to sleep. She is very petite but growth is good. During the day eats 3-4oz every 2.5-3hrs. She has slept through the night several times before so I know she can do it. Am I still feeding on demand at this age and am fighting an unnecessary battle? Or what should I be doing bc I’m gunna lose my mind if I don’t get more sleep soon.