Kay you might want to call a pharmacist to see if he has any glues that are designed specifically for healing wounds. They may be a little more expensive than Super Glue but a little more gentle to the skin.
My teacher uses a technique similar to the one Carl has described, but I can never seem to fix the tape so that it doesn’t catch the string.
If you attempt to use a glue, hold the slit together gently and paint the smallest amount over the top of the slit, then hold the slit closed gently so that the glue can take hold. If you get much of the glue into the slit, it can sting like purple blazes.
Before bed, cover the wound with antibiotic jelled salve and bandage it. A lot of healing can occur during the night.
I’ve had a split index finger for about 3 weeks. I get it almost closed, play for an hour and it opens again.
Hope it’s much better soon!