So a little bit less than a year ago I made a decision (unfortunately) to dye my hair red. It looked really good but then a few months later it went orange, so to look less like a redhead I dyed my hair brown (box dye) and I kept that for a few months. I recently went to the hair salon (about 2 months ago) where I got a base color which was a brown, and a full head of highlights. I'm ready to go more blond now because my roots are growing in.
Right now my hair has a little bit of a hint of red in it, so I'm worried if I do decide to box dye it blond, it will end up showing through more than it shows now.
So now, my question is, should I box dye my hair more blond or should I get it done professionally? I'm not looking to spend hundreds of dollars, I need a cheap solution. I have box dyed my hair blond before and it looked pretty good so I'm thinking of taking this route.

Opinions, advice and concerns are more than welcome

Thank you very much in advance!