I also get pins and needles in my feet after about 3 miles which continues and gets quickly more painful until I stop running.
I also have pins and needles in my hands, specifically the third and fourth fingers and worse in the left hand. This has been diagnosed as temporary nerve damage caused by leaning too much on the elbow or having the elbow bent too much, particularly having it bent all the time you are asleep. Leaning on the elbow causes the nerve to get sqashed and having it bent for long periods causes the nerve to be permanently stretched. These things over time causes damage.
The pins and needles in my hands gets worse when I am running, probably because the arms are bent and moving, aggrevating the nerve.
I doubt your fingers will off but you should look at things like how much you are leaning on your elbows and whether you have them bent for long periods like when you are asleep, and try to correct these things. If it is the nerve, it should return to normal.