Is the edge of the glass sharp / from being "cut" or rounded ?
If it's sharp / rough to the feel ( it's been cut and not polished ) this will cause injuries. Is easy fixed if you get a glacier to visit and "fire" polish or use very fine abrasives to polish the edge.
You can mechanically polish the glass edges , a visit to the hardware shop to get a tub of aluminium oxide or cerium oxide rubbing slurry, this will polish away the "roughness" and any sharp angular edges and make the glass edges much less likely to cause this kind of injury in the future.
I've had success with fire polishing ( of glassware , a laboratory skill ) and mechanical polishing ( glass sheets etc ) .
Mechanical polishing using slurries of very fine Al2O3 and CeO2 is slower but can produce very smooth surfaces and wont effect the temporing of the glass.