Is it possible to get a milk intolerance after giving birth to a lactose intolerance baby

When I got pregnant I could drink milk I would throw it up. My baby was born not being able to drink regular formula caused tummy cramps and very weird poop. Switched to soy and it improved. Well 2 hours ago I drank a cup of milk and 20-30 minutes later my stomach started hurting and I went to the bathroom and I had diarrhea. This happened once before but I dismissed it because everyone in the house was sick. Am I stupid or can that cause a dairy intolerance?