What would cause my fingertip to turn purple,swollen hand and finger with no injury.but i do have poor circulation in hands and feet.been like this for almost a week?

In the absence of injury these could be signs of an autoimmune disorder causing disturbance in circulation of oxygenated blood to your hand and finger. I would consult a rheumatologist who may also want you to be evaluated by a vascular specialist.

A vascular Raynaud’s like process appears likely where there is an exaggerated vascular/ spasm/ constriction response to stressors. Start with your primary care doc for an exam based on which further work up and possibly a referral can be coordinated locally.