I agree with the ortho-
Thatdoes sound like a nerve generated pan, and an MRI would help,
But in the meantime, have you tried using a finger cap (like a splint you can buy in store)
If this can eliminate the pain, it would be quite helpful.
Otherwise, short of a neuroma ( a bundle of inflamed nerve tissue) I cannot thing of anything else that would cause this. These are handled surgically, but you could avoid surgery with a fingertip splint, and you could try a round of nerve pain medication such as gabapentin, or lyrica. They are Very helpful in situations such as this.
I recommend trial of a finger tip splint/cap,
And asking your doc (if splint is no help) for an rx to one of the above.
If no help, or it worsens......Yep- MRI is what you will need.
I hope this was helpful-
Feel free to ask anything else to clarify-
MyBest and happy holidays!