Carpet Burn caused itchy patch that won't go away

About three+ years ago I got a nasty carpet burn on my lower back (don't ask how) - the skin was peeled off, basically.
I never got chance to clean the wound properly, I just let it heal, so it probably healed over with particles of whatever microscopic crap was in the carpet :(

Post-healing, a really itchy patch of skin developed ABOVE the original injury site - and is still there today, just bigger and itchier than ever.
The original burn area is just slightly darker than the rest of my skin, but this "Rash" is just above that, and about the size of 5x3 inches in size, with little bumps that really itch. Occasionally it turns scaly and dry.

I have been prescribed a couple of different steroid creams and an emollient cream, which I have applied as instructed, but the patch does not ever seem to go away, and has just increased in size over time. The doc did act slightly confused by the "rash".
Like I said, it's been more than 3 years and it is still there.

It's the early hours of the morning here and my mind has wandered onto the possibility of a more sinister condition caused by toxins or whatever in the carpet. Why are the creams not helping it?!
Could the wound/burn/abrasion along with the carpet created some kind of weird skin condition / cancerous lesion?! :(

(I'm 33, female)

Thanks in advance.