It is difficult to say whether you have broken tooth or not with out seeing the X-ra and the clinical examination. But if it is bothering you then definitely it will be infected and you can go for root canl treatment. Whether root anal treatment is possible or not depende upon the extent of infection and the tooth material. The cost of root canal treatment for the back tooth is $1000 to $1100. Above ths you have to go for the crowning which will cost another $1000.For more info on root canal treatment you can visit the following link on our website......http://www.identalhub.com/articlecategory-root-canal-therapy-17.aspx