WIC should not need a doctor's note to know that he is lactose intolerant. They don't in Fort Wayne Indiana. He may have acid reflux. Pediatrician's can prescribe something. You might also consider putting him on an over-the-counter to see if it helps.
Many infants have an under-developed flap on top of the stomach. It makes them spit up whenever they lay down or lean over. In that case, the child needs to sit up for 45 minutes after eating. I used to put my infant in the car seat inside his crib, in a bouncer, in a walker, in a jumper in the doorway or I would wear an infant carrier. At night I used to sit up holding him, so he wouldn't spit up. When that became too tiring, I would fasten him into his car seat carrier and put it inside the crib. Also, it becomes dangerous when an infant spits up a lot because they can choke if they are laying down.
My son had problems with acid reflux and an under developed flap on his tummy. I tried all different kinds of formula, and nothing really helped. I finally ended up putting a teaspoon of cooked formula into his bottles, and he spit up less. It used to be like a fountain that would spurt out. After putting the cereal in his bottle, starting at 1.5 months or so, he finally started to put on weight. Then he only spit up maybe an ounces or so. I still had him on the meds and sitting up all the time. So the combination really helped.
You might try getting onto Hoosier Healthwise, which can be free insurance for children or dramatically discounted. Many health clinics give free immunizations. Business Health Clinics and Redi-Med near Cook and Coldwater Rd in Fort Wayne have free immunizations from 9am to noon on Saturdays. Since you will already be there for the immunization, you can ask other questions of the nurse. Usually they will ask the pediatrician or doctor in the office for free. You might also try calling the pediatrics department of a hospital and ask for the on-call doctor. Sometimes nurses of pediatric offices will answer questions as well.
You might consider supplementing your son's diet away from formula to more solid foods. At 4 months many children start eating the number 1 Gerber foods. You could try replacing a meal with mashed-blended potatoes, yams, carrots, bananas, applesauce, baby cereal, etc. Try to leave out the dairy and see if he still spits up.