Every gunshot produces a noise that could damage the ears of anyone in close hearing range. Large-bore guns and artillery are the worst, because they are the loudest. But even cap guns and firecrackers can damage your hearing if the explosion is close to your ear, and pistols are worse than rifles because the end of the barrel is closer to the ears. Anyone who uses firearms without some form of ear protection risks hearing loss. Not unless you mean a pair of professional, wax-impregnated cotton earplugs.
Ordinary cotton is much too porous to provide any protection at all.
Most sporting goods stores sell them at a modest price. They should be fitted separately for each ear, because each ear canal might be a different size. If both plugs fit snugly, they can provide about 15 dB of noise protection. Hearing specialists recommend muffs for anyone who works in construction, mining, lumber, or any other noisy job. Muffs can also provide protection for target shooters, hunters or anyone who uses power tools or noisy yard equipment.