I had always sung, from just backing vocals up to half of the lead vocals but my voice only really started to develop once I stepped up to be main vocalist. I'm not a natural singer, I don't have exceptional vocal chords but I could feel and hear my voice growing in range, power and subtlety.
My advice is to sing as much as possible. If it's a rehearsal then just go for it, if the rest of the band really want you singing they'll put up with a few dodgy moments. Hold back at gigs until your confidence and hopefully ability grows.