Not a pheasant mix, that's probably due to her 'mixed colors' but that's all chicken genetics and colors.
She seems rather Gamey to me as in american game(aka breed used in fighting). Games can be bred without much regard for color so they can throw quite colorful birds.
it sometimes seem games are one of the most common found/dumped/breeds at shelters. Some probably are accidental escapees while being transported- they can be quite good at escaping if so inclined.
Her comb is not red, which means she is not in laying condition yet. Don't expect eggs from her real soon.. but she will eventually lay. If she's a game, they are often fair layers(don't expect as many eggs from say, a barred rock) and very prone to going broody.