Many years ago I crushed my index finger of my fretting hand under a very heavy belly plate of a Cat D9 bulldozer.
It was agony. I went to the hospital to get it checked and they just dressed it. No stitches.
It took ages to heal and at one point the doctor told me that it had become infected, and it was possible I would have to have the top of my finger removed.
We were very busy with playing at the time and I was terrified.
Luckily it was ok and gradually healed.
I have been left with a wonky looking finger tip now and the nail grows off to the side.
Again, this took a long time before I could comfortably play with it, but my mate, the guitarist insisted we play a gig we had booked less than a week after I had done this. I said I can't play with this. Oh, you'll be fine, he said.
Foolishly I agreed and had to play trying to avoid using that finger. It was a horrible experience and probably put my recovery back, because muscle memory kept kicking in and I would fret my index finger, which resulted in a lot of pain shooting up my hand.
I am also the singer so this made for some strange noises coming from the PA.
All I can say is let your injury heal itself and don't try to rush it. It will take time, but you will be able to play again.