Should i go to the doctor for my burn?

a week ago someone burnt me with a lighter. it immediately started to blister and fill with pus, since then it has scabbed over but it won't heal up. the scab is greenish yellow, and it is very pinkish red all around the burn. it hurts all around my arm very badly even when i'm not touching it, it hasn't gotten any smaller or less painful. it's definitely a second degree burn, i just don't want it to get worse. any advice?