I have severed several tendons in my dominant hand. 6 to be exact. Two separate injuries with the most recent one being the most severe as I spliced five tendons (middle, ring, and index) and then ended up re-rupturing two of the surgically repaired tendons which required a second surgery a couple weeks after the first. The first was the upper tendon in my index finger but that healed up real nice. I have full function there almost 20 years now. Not so with the recent one. I'm older so my body probably doesn't respond to healing as well as it did when I was a teenager. It's funny because it took a shard of glass, not even a 1/4 at it's longest point, to do the most damage. That itty bitty piece got five tendons! D-A-M-N!
Adjusting has been tough. My baby was born around the time I spliced them so I was unable to pick him up for a very good length of time, I struggled to communicate with my wife and older son (both Deaf). Devastating for me as I did not want to miss that critical age where the bonding happens (fortunately, he turned out to be a daddy's boy).
It's been three years since the injury... and I still struggle with it. Even today, people definitely notice my hand. Additionally, I get a little self-conscious about meeting new Deaffies as my signing appears "rusty" when it really isn't. I'm unable to fully extend my pinkie and ring fingers. It's mostly my ring finger that has healed disfigured. I have a ton of scar tissue and swelling of the joints. It's certainly painful from time to time.
Despite me being self-conscious (which I think is normal)... It hasn't stopped me from signing though. Bottesini is right. The people you talk to the most will get used to it. It is now your mark and contribution to your own version and beauty of ASL.