Hi good morning as I can understand from your question one of your molar teeth has got severely decayed. In technical terms we call it grossly decayed teeth. The pain in the teeth is because of the infection affecting the nerves of the teeth. Generally if the nerves of the teeth get involved we suggest root canal treatment but in your case since the tooth is badly damaged I would advise extraction.
Next Steps
Since you are young dental implants would be a good option for you. We have something called as immediate implants where we extract the teeth and place the implant in the same sitting.
Health Tips
Depending on the quality of bone you can get the teeth replacement on the implant from 6weeks to 3months.