How long can I wait with tingling to see if it goes away without seeing a doctor?

No wait. Tingling can be caused by minor cause to life threatening cause. See your doctor soon.
Tingling. Tingling is not an urgent symptom. If you do not have any pain or impairment of function in the related extremity, you can safely wait until it is significantly bothering you. Most tingling is caused by irritation to a nerve. A common example is carpal tunnel syndrome; another example is diabetes with injury to the foot nerves. If its really bothering you, see a doctor for medication to help.