The symptoms show that you may be having lactose intolerance. That means you have no or very little lactase to metabolize lactose. Undigested lactose stays in your stomach and intestine to give problems and this also results diarrhea.
60% of the world population has lactose intolerance or milk protein allergy. If you avoid milk completely the symptoms disappear very quickly. After that, try with very small quantities of milk or dairy products to find out the amount that may be acceptable for your body. If there is no lactase present in your body look for soy milk.
You must be careful in taking processed food as most of these contain milk powder or dairy products. In extreme cases all the food must be avoided with milk or dairy products. This is applicable to ice cream too.
If you have further problems after avoiding milk and dairy products go to your doctor for a complete check up.