Median nerve cut not healing correctly? stitches. relatively superficial cut, improved at first, 3.5 months later can't feel middle finger. doc visit?

Yes: Where was the cut? Median nerve is deep. Superficial cut would not involve unless cut was on finger itself (wherein nerve would be a digital branch of median nerve, not the median nerve itself). In any event, need evaluation since nerves are important. Check carefully if both sides of the finger are involved on only one side. Report to your doctor. (If image: not included by me.)

Be careful: Yes, do check in with your doctor, but do be aware that the nerve grows back slowly, about 0.1 mm per day. Nonetheless, have it checked just to ease your mind.