If my teeth hurt when chewing do I need dentures?

No. See your dentist. Your own teeth are almost always better than dentures, but you have to take care of them. If the pain is due to a mouth full of rotten decayed teeth, then something may need to be done, but extractions are a last resort. A good dentist can advise.
Likely not. See your dentist for a full examination including x-rays to determine the cause of the pain. May be a number of things going wrong. Best not to wait, or things will get worse.
Not necessarily. If your teeth hurt you need to see a dentist to determine the cause of the discomfort. The cause of the problem will dictate the treatment.