Is it weird to be scared to drink water because of teeth demineralization that has started from not brushing?

Yes: Drinking alkaline purified water is a healthy choice for many reasons.

Possibly: If you teeth are sensitive to hot and cold water from the destruction from not brushing than that is why you might be scared of drinking water.

Water: Remember that water is healthy to drink. Soda, juices, iced teas and many other beverages contain the acids and sugars that demineralize your teeth. You are doing something good for yourself when you drink water.

What to do: Have your teeth fixed so you will be comfortable and not have to worry about drinking water. In the meantime just avoid very cold water and sweets. Start brushing and flossing properly so you won't have cavities or gum disease. Have your dentist go over these techniques with you to make sure you are doing them correctly.

That depends: On why you are afraid to drink water. If it is because the water is to cold, then no, it's not weird, just warm it up a bit. If you are afraid that water will cause additional damage, then yes, that's a bit weird, it will not damage your teeth and is in fact the least damaging of all drinks. Please see your dentist to address your concerns in person.