If when you bend the last joint on your finger you have pain, yes ths could be arthritis, and likely has been there all along. If the problem is at the ry tip of the finger,it is rather uusual, and you are best following the recommendatons of the ortho.
Have you had blood tests looking for arthritis?
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!