No, STDs, including HIV, need a human host in order to transmit. You need to have either direct genital skin to skin contact (or oral to genital) to transmit, or mouth to genital, genital to genital, or genital to anal penetration.
You might get a yeast infection, or staph or MRSA though. Those live longer outside a human host. None of those would cause a green discharge, though. I wouldn't overly worry about this. I can't think of a vaginal infection that causes a green discharge.
Next time, maybe wear underwear. :)