Semi permenant colour does contain peroxide, and some contain ammonia as well, and the ones that dont tend to have a higher concentration of peroxide. So yes, they do affect the condition.
I had similar problems many years ago except it was my own choice/doing as I'd been going to a hairdresser for scalp bleaching (basically bleaching my hair to a white blonde) - I was young and fresh faced and I could get away with it! (think Gwen Stefani in her heyday)
Anyway, stoopid hairdresser overlapped it and because she was using Wella Coco (which is supposed to be for afro hair!) it fried it and it started breaking off about an inch down, at the crown. You can imagine my horror.
I had very little options. I had to wear it in a ponytail basically, because it was the only thing that was able to disguise (in the most part) the fact that my hair was breaking off, though I did have some breakage at the nape of the neck too which looked really silly but as it grew I could just kirby grip it to the rest.
I thought I was going to have to go cold turkey and just let it grow out but I couldn't bear it. I went to Nicky Clarke salon in Mayfair and had a really good bob cut. That was a start. When I had about 2 inches of roots, I dyed the roots only, bringing them up to a light golden brown (I am mousey naturally) and was able to match the body of my hair using "temporary" colour which just coats the hair shaft and doesn't damage it or use peroxide.
After about 6 months and a few more haircuts I went and saw a hairdresser in my home town who did a combo of lowlights and highlights and gave me a really nice neutral highlighted look which wasn't too blonde but was much better than anything I could do.
You are probably not in quite as much shit as I was but if you are really hating your roots you could look at bringing the body of your hair down a few shades or just say sod it and risk having the body of your hair matched to your roots so you can go natural. I liked the previous poster's idea of having some lowlights weaved in, that's a good idea and will make the graduation more natural looking.