Hey Maeghan, ive had the same problem ever since i died my hair brown last year. I am naturally brunette but at the time of getting my hair died my hair was blonde. The brown looks great inside but as soon as im out in sunlight i get a yuky red tinge come through my hair. I dont really know but for me this red tinge has been impossible to get out. I have redied my hair many times over the last year and i always end up with the red tinge not to mention i always end up getting the colour darker than i want it just because i dont want to risk having the red. I like my hair brunette i think it really suits me but im thinking now of just going blonde in summer because i dont think i can beat this red.
Things may be different for you tho, ask your hairdresser to put a brown colour in that will over ride the red. Hopefully this works . Well good luck, hope to hear how things turn out xx