I had a virtually identical injury to the third finger on my right hand.
Trapped my gloved finger in a moving hydraulic part of a mobile crane.
Squashed it flat without breaking the skin, broke the last bone just next to the knuckle same as you. I hope you do better than i did. Took a very long time for the break to repair, my physio said that in all probability the bones wouldn't knit together again because of splinting difficulties and movement. She said that most likely a natural cartilage substitution would create a bridge between the two. Three years later the joint is a bit lumpy and different, but the pain and tenderness has gone and it works almost
as well as the others. See, there is light at the end of the tunnel,its just that it might be a very long tunnel.
Good luck,
Frank.