I have severe pain with cold water in my upper right lateral tooth , this is why ?

Tooth pain: Sensitivity to cold can be from tooth root exposure from recession of gums. It also may be a cavity. As a cavity gets bigger, the nerve in the center of the tooth can become inflamed (reversible pulpitis) causing sensitivity to cold, and sweets. If this condition continues you should see a dentist very soon. Especialy if it is severe pain. An infection may also be brewing. Good luck.

Bite issue: Did you have braces? Sometimes afterwords abfractions can happen, which is enamel flaking off of the tooth. Loss of attachment and recession of the gums can happen as well that will make your teeth sensitive. A bad bite can do the same. See a dentist, especially one that has bite training and a working knowledge of orthodontics will better explain this to you.