Breast engorgment!

Had our baby girl Nov. 23rd at 39 weeks. 5.10oz. Yesterday my milk has came in full force. I’m not breastfeeding due to medications I take. I remember going through this through my last but not that it hurts this bad. The pain is insane and they say not express just leave them alone if you are drying them out... but I don’t even have to touch them for them to leak streams. I’ve been icing ash much as can, taking ibuprofen and Tylenol. It’s so hard to do daily task taking care of my 2 year old and a newborn... and on top of that I have a lovely hemorrhoid. Any advice would be great! Or anybody else struggling through the same?