In the US, "local chemist" translates to pharmacy.
A popular product with salicylic acid for ingrown hairs is Tend Skin. It's not available in retail stores. You'd have to get it online or from a salon. There are other products in the shaving area of your pharmacy.
There are 3 modalities of electrolysis, galvanic, thermolysis, and the blend. Galvanic is a DC current, when applied causes decomposition of the dermal papilla. Thermolysis is AC current, when applied cauterizes the papilla. The blend is a combination of the 2 currents.
Does it hurt badly? No. But you will feel it. "Expensive" is a relative term. For some it's not worth $100 to be hair free. For others, being hair-free is priceless. Electrologists charge by the amount of time each treatment lasts.
Electrologists work out of private offices, physician's offices, salons, or their home. If you have a dermatologist, ask if he/she can refer you to an electrologist. Fayetteville may be too small for an electrologist, but you are close enough to Atlanta to have many to choose from. Check your phone directory under "Electrolysis" and "Hair Removal."