I had a Perfect Derma Peel done and I started peeling on day 3. I peeled a skin manually

Hi!Hopefully the area will not hyperpigment, but it's a possibility. It can be very tempting to tug at the peeling skin, but never a good idea. When getting a peel you need to plan to have down time and let the skin peel/flake off by itself. While your skin is healing, use a gentle cleanser, moisturizer as needed, and wear your daily broad spectrum sunscreen. If the area does hyperpigment it will fade with time. You can add a retinol to your evening skin regimen and this will help with hyperpigmentation.Regards,

It is not normal to have uneven skin pigmentation ...
An appropriate chemical peel may help start the process of treating uneven skin pigmentation.
For uneven skin pigmentation I also recommend a skin regimen:
Melarase AM cream is great to reduce hyperpigmentation and to correct uneven skin pigmentation.
 I also recommend Pigmentation Correction Complex to reduce hyperpigmentation of the skin.
Also avoid sun exposure to prevent inflammation and skin burn injury for at least 4 weeks. Spectrase is highly effective. 
Best
H Karamanoukian MD FACS

I know it is difficult to not want to peel the skin, but it is very important to let the skin on its own. If after the skin is healed from the peel and there is hyperpigmentation, it can be corrected with products, treatments or both. 
Give yourself 7 days and if you still have concerns then discuss options with your provider.
Hope this helps,