Is a root canal necessary in my case?

You have good questions. I cannot verify that you need a root canal without xrays. However, based on your mentioned symptoms it certainly seems you need one. As to whether you should use a specialist or a general dentist, I cannot say as I have not seen your dentist's root canaled cases. You should know that most dentists are trained in delivering root canals and if they are comfortable with treating your tooth then it may be successful. Specialists are very good and I do see a quality difference in general dentists vs the specialist. In full disclosure, I do not do root canals because my skills are not as good as a specialist. This in no way reflects on your dentist and his/her skills. If you are confident in your dentist's abilities then it should work out successfully.

If  the x-rays shows an area of infection  you would likely either need to consider a root filling  or alternatively  an extraction to resolve the infection.Its difficult for me to be sure without seeing the x-rays and examining you.
If you decided to root fill the tooth  and depending on how difficult the root canal of your tooth is to fill your dentist may be able complete the procedure or if they feel it too difficult may recommend a  referral to an endodontist who may have access to a microscope to complete the procedure.

I have my all specialist in each case because it is not the same. Xray complete a part of diagnosis but there are others proof that is used like: cold test, hot test, touched the gum in both side, and make a percussion. 
Best of luck,
Dra Alfonsina Hdez R