If I drink more than 1l of water I get an awful migraine. If I exercise and then drink water afterwards I get nauseous, shaky and have to lay down. Why?

Migraines are very. Different in different individuals. Some people may have various behaviors which incite a migraine. Do you think it is the cold water that causes the migraine. It is not likely the water itself is causing the migraine. But more likely a change in body temperature or perfusion of your brain. When you drink water after exercise you might get a different migraine. It might cause nausea.