Before digging re-evaluate to see if you really have a piece of glass or not.
Many times barefooters will have a sensation that there is a piece of glass, but really it is just a temporary nerve stimulation that eventually goes away.
Every time in my early days of urban barefooting that I thought I had a tiny invisible piece I dug and dug but never found a thing. After healing of the iatrogenic wound I was fine.
Many SBL members found the same thing, a "phantom" shard of glass that wasn't really there.
But Doc WDC is correct, if there IS indeed a piece it may cause problems (or it may not and just remain where it is problem free)
Do you feel the pain/discomfort with every single step? Is it always the same intensity?
I've found over the years that when you have a piece you REALLY know it without doubt, where with the phantom shard occasionaly it is a weaker sensation.
Also, when I push on the spot with my hand I feel nothing, but with the true shard I feel intense pain even to the light touch.
Good luck and keep us informed with of the outcome.