Soreness after laser hair removal is better treated as a short set of rules you were handed and should follow than as a home-care project.
Soreness that feels like sunburn
DermNet describes a sensation of a mild sunburn, with redness, peeling and swelling, that may last a few days after treatment. The comparison works in one direction only: it tells you what to expect, not what to put on it. For the technology behind the treatment, DermNet's page on Nd:YAG laser treatment is a reference for one laser type.
Sun exposure is the variable you control
Sun is an everyday variable that sits in your hands. The Skin Cancer Foundation's page on sun protection is the reference for the basics, and your clinic should tell you how those basics apply to treated skin.
Products can change the sun question
The Skin Cancer Foundation also publishes Is Your Beauty Routine Making You Photosensitive?. Read it as a prompt to ask your clinic before you add or keep any product on treated skin.
Where the home rules end
The Skin Cancer Foundation also has wider skin cancer prevention material, but laser aftercare belongs to your clinic. Follow the written instructions you were given, and call when redness, peeling or swelling is not what your clinic described.