My daughter had issues with full lactose formula when she was younger, but didn’t have a milk allergy. Gerber Soothe was the ticket for us. It’s still milk based, but seemed to be much gentler on the tummy than any version of Enfamil or Semilac.
As for constipation, that baby cereal crap we were told to start on at 4 months was TERRIBLE for blocking up my daughter. We instead started with boiled and puréed sweet potatoes mixed with a little formula. She LOVED it, and it kept things moving. If neither of those work, you should be fine with a little apple juice, but not much at all. We did 1 part juice to 4 parts water at 4-5 months, and it did the trick. Hope that helps!