I Have A Middle Finger That Won't Heal..months Ago Started

i have a middle finger that won't heal..months ago started as a split near tip of finger from cold dry weather
Happens to several fingers yearly. It has turned into just a sore finger that hurts all the time and worse if
i touch something..looks like maybe a blood blister in the middle although not dark as have seen in past
but bright red..will bleed when bumped..tried antibiotic cream, taping up so skin doesn't get dry and hard.
took a 5 day course of cephalexin as it looked infected and spreading up finger..just won't heal