Numb feeling in index finger?

Some time ago I cut myself on a piece of glass and the wound was on my index finger.

I covered the wound with a plaster, so far so good.

Now I have a numb, tingling feeling in that finger, since the cut to be exact.

It feels like the tip of your finger has fallen asleep.

But the feeling only occurs when I touch something with my finger.

What could this be? You can't go to the doctor because a finger feels numb; it's only the tip of your index finger.