For laser hair removal, side effects belong in the decision to book, before the appointment and not after.
The short list
Penn Medicine says you might experience minor side effects such as blisters, burns, or changes in skin tone. DermNet's page on Nd:YAG laser treatment is one place to read about the technology a clinic may use.
The longer list
AAD lists blistering, herpes simplex (cold sores) outbreaks, infections, scarring, and skin lightening or darkening as other possible side effects, and says that in time, skin color tends to return to normal. That last clause is about skin color only. It says nothing that makes the rest of the list optional reading. DermNet's page on intense pulsed light therapy (IPL, flashlamp) covers a second technology, so ask the clinic which one it uses.
What you handle at home
None of these items is a self-treatment project. If one appears, call the clinic. UCSF Health has a page on laser hair removal that is worth reading before the appointment.
The rule before booking
Ask the clinic which of the listed side effects apply to your skin and your technology, and how to reach them afterward. If the clinic cannot answer, do not book.