If you're really that frightened about the shot, you can tell them not to give you local anesthetic injections first. They are obligated not to give you a medicine if you refuse it. The problem is, when someone begins extracting a foreign body from your foot, you're going to have far worse pain than the lidocaine injection ever thought about being. You can also ask them to apply some cold spray or topical lidocaine gel to numb the spot before they inject you.
You won't be allowed to administer lidocaine injections to yourself, and you shouldn't attempt self-extraction of the glass. If you take a sharp object and begin digging around in your foot on your own, you risk getting a bad infection or injuring yourself more severely. Someone who knows sterile procedure with good light, a better angle, and suitable instruments needs to do the extraction to make sure the entire glass shard is removed and the wound properly cleaned and dressed afterwards. If you attempt it on your own and cause a wound infection, that'd make the ordeal you'll be facing far worse than what you're dreading now. Hilder is right. Cellulitis. Sepsis. Gangrene, even. Bad mojo, that stuff.
Just go. You'll be glad you did. Glass in the foot doesn't go away or stop hurting, especially if it's in a weight-bearing area. It just embeds itself deeper, which ultimately makes it worse to take out when you get around to facing reality.