Engorged hard and painful!! Need advice

I just had my little man 3 days ago and started breastfeeding right away. Last night I had to stop because my nipples were in so much pain. Latching issues I'm going to see a consultant and go to a support group for that issue once I can nurse again. I woke up this morning in alot of pain and my breasts hard and lumpy. I talked to the lactation consultant and she told me to pump every 3 hours until they are soft and non painful and to put a cold compress once I'm done for the swelling. I've pumped twice now and each time for atleast 20 minutes until no more milk came out but my breasts are still in pain and hard. Cold compress isn't helping either. I don't know what to do other than continue what she told me. Is there anything else I can do that will help my breasts return to normal that anyone has done and it worked? I want to get back to nursing my son asap especially since he's not handling formula or the bottle well and spits up so much no matter what. Enfamil newborn formula with tommy tippe breastfeeding bottle,extra slow flow nipples and I only let him do 3 sucks at a time so he doesn't get too much at once. Lactation told me to do this so he won't spit up as much and I'm feeding him the right amount too but he still spits up and even had a scary choke attack from spit up trying to come up. Feeding is a nightmare for us and it shouldn't be. The only thing that worked was nursing. He never spat up. Formula isn't working. Breastfeeding has come to a sudden pause because of the latch issue and now this engorgement pain. I can't get any relief anywhere and am so stressed out.