M.P.
At 11 your parents or guardians are responsible for your well-being. Pain in a tooth can be serious. Have you talked with them?
Is this a permanent or baby tooth? If it's a baby tooth, it will come out. It may be painful because it's hanging in there by it's roots and you can encourage it to come out by wiggling it. I don't remember anyone your age having so much pain that it interrupted their play or meeting their responsibilities.
I have known adults to have that much pain and when they went to the dentist learned that they had an infection in the gum. Is your gum swollen or inflamed and perhaps just a bit warm? If so, I suggest that you talk with your parents again. If you have an infection eventually your cheek will feel warm to the touch, you'll have a fever and they will be worried and call your doctor.
If this is a permanent tooth, how did it get loose? You said that you think a root is broken and the edge is sharp. This makes me think that your tooth has been injured. If someone has hit you or knocked you down and your parents are not taking care of the injury then you should call Child Protective Services, CPS, for help. Look in the blue pages under the county government heading or call directory assistance.
If the reason you can't go to the dentist is that your parents don't have the money to pay one then they can take you to a county clinic which will charge on a sliding fee scale based on their income.
You deserve to be taken care of. I don't know what happened to your tooth but if it's a permanent tooth, from your description, I think you may loose the tooth and it'll be gone forever unless you get treatment.
In the meantime, chew a piece of gum and when all the taste is gone wrap it around the bottom of your tooth so it won't rub on your tongue. If it's a permanent tooth, do not chew on that side and don't wiggle it.
I do hope that your parents will understand and see that you get the treatment you need. If they are concerned and have looked at the tooth and in their judgment feel that it's OK and they weren't the ones who injured it, then I wouldn't be concerned. The tooth will heal. It's if they aren't concerned or caused the injury or think they can't take you to the dentist because of lack of money that I'm concerned. Help is available.