You can be lactose intolerant too, but if lactose
free milk makes you feel sick, just avoid all
milk in general. You can maybe try drinking cream instead of milk if you want, or putting cream in coffee or tea instead of milk. Don't eat foods that make you feel sick, it can cause major health problems in the long run.
I haven't really experimented with only eating cream, but I am going to try. Also I am not a doctor, just very observant and really smart.