Will hypopigmentation caused by laser hair removal go away? What can I do?

There may be a way to get reassurance from a dermatologist who can use a Wood's light to see if there is porcelain-white color or just lightening in the skin patches. If it is just lighter than there is a good chance it is hypopigmentation and not depigmentation. Use sunblock to avoid getting accentuation of color around the white spots and also to avoid getting a sunburn on the white spots. It can take months for this to come back to normal.

Unfortunately it is difficult to predict whether your skin will return to its normal pigmentation. Sometimes the pigment does return to normal, but depending on the laser used and the depth of the burn, the hypopigmentation can be long-lasting or irreversible.

How long ago did you have the laser treatment done?  What type of device was used?  And on a more encouraging note, even though your photo is blurry, some spots look like they are repigmenting.

I recommend returning to your treating physician for an evaluation.

There is a good chance the skin will re-pigment but it all depends on the depth of the burn and your skin's ability to repair itself.  Only time will provide the answer as there is nothing I would recommend doing at this time to speed up the process.  Be extra careful with sun exposure to the area for quite a while.  You  have lost your natural protection in that area and the skin can burn very easily.  A sunburn may only worsen the problem.