Help! 4 month old with acid reflux doesn’t nap or sleep!

Okay so my 4 month old DOESN’T sleep. He refuses to nap during the day. If he does they are cat naps 20 minutes. It makes it impossible to get anything done.

At night it takes sometimes two hours to settle him down. In the night he’s average up 3-4 times. He’s a breastfed & formula baby. I like to breastfeed only at night, I feel like the formula bottle wakes him more.

He has GI issues. Bad acid reflux & has been on Zantac for months. He’s slightly underweight so the dr has us follow up more. We’re gonna start rice cereal soon so I’m hoping that really helps. Sometimes I can tell it’s bothering him & feel awful so just wanna hold him & ease his discomfort.

He’s a light sleeper. Even if he falls asleep in our arms when we transfer him he wakes immediately.

I feel like he’s still so young to cry it out at all, but open to listening to all suggestions. The dr said we can start sleep training but don’t let him cry excessively (1 hour) I was also told to start cutting out his night feedings. She said he should start sleeping 6 hours at least (Hah!)

He’s my second but my first didn’t have this problem. I know it will pass but does anybody have any suggestions or advice!?

Even my in laws were like wow they’ve never met a baby that just doesn’t nap!

He is a happy baby for the most part & my miracle after three miscarriages so of course I’m smitten I mean look at that face 😍😍