No, drinking milk or water after eating watermelon is not healthy at all because it can cause tremendous chemical reaction in the digestive system, which can cause the stomach over expand with gas resulting into stomach ache and can result into vomiting and indigestion. Stomach ache occurs mostly when you eat this combination in the morning.
It can also cause some allergies like itching and scratching in throat.
If you ate the combination in night then beware it can cause sleepless nights.
So, try drinking milk and eating watermelon separately. Eat small amounts of watermelon because it contains acid that causes gas and don't eat seeds.