Is it normal for a sewing needle foot puncture wound to take a long time to heal?

No: See a podiatrist asap. Don't play around with puncture wounds. There could be a deeper underlying infection etc. How about tetanus history? Any sore/ wound that doesn't heal i a healthy person should be seen sooner than later.

Depends on a lot: Is the needle or portion of it in your foot? An infection can cause delayed healing and pain. Did you have a tetanus shot in last 5 years? Are you diabetic? Those with poor ciculation or immunocompomised will have delayed or no healing. By the way, how long has it been? An uncomplicated stick from a needle if cared for properly in a healthy person should heal within 10 to n14 days.