Hi, Well, it looks like you have lost the entire crown of the tooth and the part of the tooth that is remaining is the roots of the tooth. As you said you have pain and sensitivity to hot and cold then there is a possibility that you have re-infection in tooth as well as gums. There must be food accumulation in that area that can further add up to infection. Hurting head by the eye is radiating pain from the tooth only and feeling sick by stomach commonly occurs due to infection that is also being swallowed down. So the first thing that you need to do is to consult a Dentist and get a latest X-ray of the tooth done to rule out the exact extent of infection and tooth damage. In case if the tooth has only roots left then you should better get the tooth removed and get an Implant done. It will however depend on the bone density and other things that can be checked with X-rays and a clinical examination. As far as treatment cost is concerned it will depend on the line of treatment and also the quality of the materials used. So better Consult an Oral Physician and discuss the line of treatment. Accordingly the cost of treatment can be estimated. Take care. Hope I have answered your question. Let me know if I can assist you further. Regards, Dr. Honey Arora, Dentist