I assume you're living in the United States. Sorry this information is too late to be of any use to you, but it goes for anyone reading this thread inside of the United States of America.
Do not go to the ER unless it's absolutely necessary, events such as heart attack, stroke, vomiting up pints of blood etc.
Do not take an ambulance to the ER unless it's absolutely necessary. Have someone drive you.
At Urgent Care you do not need health insurance and you can pay up front in cash. Some of them operate almost like pill farms and if you just say "I need painkillers" the doctor will just give them to you without thinking twice and you pay him in cash like a legal drug dealer. I'm not saying you should exploit them to get drugs that aren't intended for your condition, but you can get pretty much anything you want there and even things most hospital doctors will be hesitant to prescribe such as highly potent anti-biotics.
If you do not follow the above guidelines you can get stuck with $250,000 in costs from a single visit if you don't have health insurance. I don't know how much you make every year, but I'm definitely not gonna be paying that off in my entire lifetime, especially when interest starts piling up. If you have health insurance, then use it. That's why you have it. If you don't then realize that in every hospital in America there's an entire section of the building dedicated solely to banking/accounting and I don't mean keeping track of internal expenses, but rather how to liaison with debt collection agencies and make sure that you pay them something eventually, even if it's ripped from your hands.
I'm not a doctor, but you probably figured that out already. Take this as my personal advice, but not as professional medical advice.
Cutting yourself on glass would warrant an ER visit if you feel numbness, loss of feeling in or near, or inability to move/use said limb (severed nerves), you have blood spurting out of the wound (severed artery) or you got some glass in your eyes and risk permanent blindness if you don't see someone specialized in that type of medicine within the next half hour. If you're sitting here typing all this stuff, especially on a phone, you're probably fine with going to the Urgent Care. They will cleanse the wound, pick out any glass in a non-emergency fashion aka with tweezers, will bandage you and give you all the pills needed to stave off infection or pain.
And don't ever think that when you call an ambulance that you're "taking it from someone else" (vaporous entity who may/may not need it more than you or is just defrauding the government). The only thing you need to worry about is if YOU need that ambulance. YOU should come first in your mind because when the spit really hits the fan nobody is gonna give a rat's behind about you anyway, except maybe your mom or dad if they're still alive and functioning in society.
Good luck with your injury.