An Aunt of mine who owned and operated a Kowalski store( mostly deli counter) sliced the tip of one finger off on one of her slicing machines. (OUCH!)
It was able to be reattached, and did too, take a long time to heal, but she never did regain feeling in that fingertip, but was able to function normally by figuring a way to use "sense-memory" of how it was normally used and didn't allow any apprehensions to cloud her confidence in normal activity.
Within the last 20 years, I've dealt with Venous insufficiency, then a mini stroke and now Lymphedema which left my left foot numb most of the time. But by sheer determination and my Aunt's example, I walk practically normally, the only effect is the dragging of the foot a bit due to the stroke.
In your case, if there's no pain in using the finger when playing, I'd put that disconcerting feeling out of mind( and I DO know that feeling).
As for the advice to "go see your doctor", well, what I've learned from my wife's troubles the last 15 or so years, especially the last two, is that there are considerable
limits to what they're able to do that really helps, what they actually know, and they find it extremely difficult to say, "I don't Know". ie: My doctor told me the numbness in my left leg, arm and the left side of my face will dissipate and be completely gone "in time". That was FIVE YEARS ago, and still no change or improvement.