I have alopecia areata and I feel pain at the paches on my scalp. Why?

In general there is no pain associated with alopecia areata. If you are concerned you need to see a doctor for a proper exam.  There is not much the Internet can provide aside from general information.

I suggest you consult a board certified facial plastic surgeon
because the board certified credential ensures you receive the highest
quality knowledge, treatment, care and skill available. Please consult a board certified facial plastic surgeon who specializes in hair treatment as well. Best wishes.

The treatment of alopecia areata is always non surgical. Dermatologists are experts in the evaluation and treatment of alopecia areata.Pain is uncommon with alopecia but burning and tingling can occur.Be sure to get proper advice from the appropriate specialist. Steroid injections are the appropriate treatment for most individuals with patchy alopecia. Topical steroids and minoxidil are also commonly prescribed.

Ypou are correct that you need to see an expert for the treatment of this condition. If the treatment fails as it often does, you can have scalp micropigmentation to treat it. See an example of SMP treatment in the web reference below. 

Alopecia areata is an autoimmune disease,  where the body's own immune system attacks certain hair follicles.  The symptoms can include pain,  stinging or soreness.  The treatment includes an internal workup to rule out internal causes. If there are no internal causes,  then the inflammation needs to be reduced with either topical or injectable corticosteroids. I would recommend you seeing a board certified dermatologist.