Although your final results may take as long as several months to be fully seen, at 6 weeks you should be seeing some degree of improvement, and most redness should be gone. You will still have edema (microscopic swelling) within the skin tissues, which tends to emphasize the residual textural irregularities or wrinkles present in your skin. 6 weeks is right about the time these are at their worst, and I tell patients that this is a very common time for the "blue funkies." Enough patients have these concerns at this time when they have returned to full work and leisure activities, and they think everything should be "done" by now. Far from that, it does indeed take a full 4 months or longer to reach final improvement. Be patient with things, and address your concerns with your doctor!
By the way, other than what your doctor told you, how do you really know it was a "deep" peel? If this healed faster than 10-12 days, it probably wasn't quite as aggressive as perhaps implied. That may well be a good thing, as less likelihood for pigmentation irregularities or scarring may be better than the "deepest" peel possible.