I would suggest these things for home care:

soak your foot (toe) at least daily in hot epsom salt water. (As hot as is safe for you.)
once you dry your foot, coat the toenail area with tea tree oil. (A natural antibiotic that works great!)
Wear clean socks, and change if they get damp. White is best. (Dyes in socks can irritate open areas.)

Good wishes!