Constipated baby advice.

I ebf from originally, then started to combi feed. When we introduced formula, baby started being sick more and was getting very constipated. He developed a bit of a rash on his chest once he started having some formula. He already had acne on his face so this could have been that but the doctor thought it was all too much of a coincidence. He prescribed aptamil pepti 1 and referred him to be tested for cmpa. This was last Wednesday. By Friday he still hadn’t done a poo which made it 4/5 days without so went back to the doctor and they gave us some lactulose. He went later that night. He now hasn’t had a poo since Friday. Even though we have been continuing the lactulose. I’ve increased by breastfeeding and really cut down on the formula to see if that helps. Im started to think to rash was just a coincidence and not related to an allergy as it hasn’t completely cleared up since he’s come of the cows milk. He has also projectile vomited a couple of times on the previous milk but that has now stopped. But that could also be related to the fact he had too much milk 🤷🏻‍♀️