Severe pain after having lactose free milk

Well this morning I ran out of regular milk but there was a bottle of lactose free milk in the fridge, so I had that with my cereal (I’ve never tried it before). It didn’t taste good to me so I only had a little bit, and I didn’t really eat much this morning. But I got to work and about 30 minutes in, I started getting severe nausea and thought I was going to throw up. About 30 minutes later the pain moved to my intestines where I felt cramping. I ended up having to have an urgent BM at work (usually I can hold it in). I’m not sure why lactose free milk would make my stomach hurt so bad, I thought it would help?