correcting hair color

My hair is originally medium brown with red highlights. In the last few years though the it has become more red than brown which, while everyone else loves, I hate. I've tried coloring it at home but after a few weeks it looks even more red. Someone told me the more chemicals you put in brown hair the more red it will look. Is that true? Also, every time I put another color on it it looks darker than I want and makes my face look extremely pale. I would love to have light brown hair but can't afford to go to a salon. Is there a cheaper way to try and fix my hair. I'm afraid to try a dark blonde color because that would really make it red. I also don't want to keep coloring my hair because it's become very damaged.