Dang, 2 weeks ago was shed hunting and got a monster of a thorn stuck in the tip of my right middle finger.
Not a raging infection or anything, but still hurts like hell when I put pressure on it. Guess I wasn't expecting to not be able to shoot due to what I thought was a minor little injury. Having draw withdrawal!
Tried pulling back with just two fingers but just making a mess of things. But found 4 sheds here in Eastern Massachusetts, one on Cape Cod so at least got some good from it.

Soak it in hot salty water. That will help draw out any infection and help relieve the pain. Puncture wounds can be hard to heal.

Keep an eye on it.  I had a thorn poke me in the lip, it got infected, and it traveled into a lymph node in my neck.  Cat Scratch Disease (Bartonella henselae) and I was sick as a dog.  Lost 55 pounds.  If you get fevers and chills in a few weeks mention that possibility to your doctor.

Lopped the last inch or so off my draw hand ring finger via a tractor accident, maybe 12ish years ago.  Ouch!  Happily it was reattached, but I could not draw with that hand for some time.  I switched to left-handed (split-finger) for 18 months or so.  An eye-opening experience.  I did get so I could shoot well enough to hunt, but no shots presented.  Teaching myself the new muscle "memory" knowing what I wanted, but mirror image, was a real learning experience and I think made me a better archer overall.

Worked up from squeezing balled socks on up to squeezing tennis balls until I got the strength and flexibility back.  It is 100%, but the pinky side of the tip has less feeling than the other fingers.  Even the nail grew back, which pleased both the surgeon and my GP.

That is a nasty turn of events! I will not complain after hearing that.
I did soak it in hot salt water last night and my wife told me to put some raw honey in it too.

I dropped a power take off shaft from a combine on my ring finger on my right hand . It split the finger, tore the nail off and broke the bone . This was just days before the bow season opened . I ended up shooting with two fingers under and I shot that way for seven years till I started to get arther in my middle finger. I found after all that time I had got feeling back in my broken finger so I went back to 3 under . Thorns can be very infectious you may need anti biotics. Ive had them before, soaking in Epsom's salts  does help .

Funny story so about three years ago, I severely damaged my left hand, mainly the index and ring finger at the knuckles, however, I recovered eventually fully, but with nerve damage in between the two fingers, manifest as greatly reduced sensitivity and some impairment in mobility. So I cannot grip the bow as hard as I used to. Incidentally, it helps a lot to not choke the thing like a snake. I then injured my string  index finger and it was so sore for so long. I forced myself to relax the index finger and not put much pressure on with it while pulling back the string and much to my amazement, I found my accuracy shooting improved about 1000%. I have never shot this well in my entire life and I think just the relaxation alone and using a slightly less heavy bow has made an amazing enormous difference so the index finger injury on the bow string hand was a massive game changer in accuracy. Oh, and watch out for Osage thorns.....

Funny this topic came up. 2 weekends ago I was helping my son on his room addition. I was cutting a piece of roof sheeting using my left hand( I'm a retired carpenter/contractor so this is not new to me) and went to grab the off fall with my right and somehow bound the saw up and it kicked and I cut the tips of my 2 middle fingers on my right hand. I'm healing up pretty good but just itching to shoot.