I have a tiny splinter in my index finger from a thorn. skin has grown over. slightly red and swollen but not painful. what should i do?

At this point likely: best to be patient. The body is usually good at slowly ejecting foreign objects as skin both grows from within & is shed/worn away. Redness= inflammatory reaction: ↑ed blood flow bringing in red & white blood cells. The WBCs work to degrade & remove the foreign object. Thus as long as you can function well with minimal soreness, likely best to allow the skin to slowly degrade & eject the material.