I would use Melarase PM cream, IPL Limelight or PDL, and light chemical peels.
I believe that there are better options than liquid nitrogen for what your desired goal was. While liquid nitrogen is extremely cost efficient with a shallow learning curve to use, it can leave a prolonged scar. It will improve with time!
I probably wouldn't have used liquid nitrogen to remove the spots. There are better options for hand rejuvenation including non-ablative lasers like Fraxel to address pigmentation and age spots and fillers for volume loss and visible veins. What you have appears to be post inflammatory hyperpigmentation and this will almost certainly improve with time. Just keep out of the sun.
Dark spots after liquid nitrogen
This phenomenon is actually quite common. The dark spots are a result of trauma to the skin from freezing, but rest assured, they will fade with time. Be sure you are using sunscreen diligently every day, whether you are going in the sun or not. Talk to your doctor as a prescription bleaching cream may also speed up the healing.
Any treatment which causes significant trauma to the skin whether it is heat, cold or light can lead to scarring. Liquid nitrogen would not be my first option to remove sun spots with the availability of IPL and other light based sources such as a q switched laser which can limit collateral damage by selectively targeting the pigment in the sun spot. Fortunately your marks should resolve but it may take several months.
Another option ion to treat the scar is a pulsed dye laser given the vascular component of the scarring. This should speed up resolution
All the best
The redness and inflammation you are experiencing will gradually fade overtime. In the meantime, be sure to use sunscreen daily and reapply often if you plan on being outdoors. You may also want to consider a treatment with IPL or laser to reduce the healing time.
Red spots after liquid nitrogen
The resultant redness after liquid nitrogen is usual and can last for more than a month. It is very important to avoid sun exposure on the areas. IPL or pulsed dye laser can help the redness fade more quickly.
Red Marks on Face -- VBeam/Pulsed Dye Laser, Yellow Laser, Yag Lasers
This is post inflammatory erythema or pigmentation. This needs skin care and pulsed dye laser treatments. It may take 3-6 months to fade on its own without any treatments. LED may help. Best, Dr. Emer.
Freezing can cause hyperpigmentation or hypopigmentation or scarring
Most of the time a gentle freeze will get rid of unwanted lentigines or freckles. Many times freezing is used to remove unwanted growths like seborrheic keratosis, warts or precancers. Liquid nitrogen is what is used to, "Freeze off" unwanted growths. There are always risks with any treatments, but a gentle freeze should leave very little residual damage. I believe that these spots will fade away. If they are red, a pulsed dye laser can be used to remove the redness. Brown spots can fade with a number of bleaching creams or a laser for brown discoloration. Good luck! H.
Treatment of age spots with liquid nitrogen takes time
These marks will certainly fade over time. Keep your hands well moisturized and protected with sunscreen. For age spots, seborrheic keratosis, liquid nitrogen is certainly the standard of care. Unfortunately the recuperation takes time.