Kinda difficult to hide. For the first few hours there's some redness and bumpiness ("cottage cheese" skin). That smoothes over on the first day, but you remain swollen for a day or two, depending on laser strength. Your parents may pick up on that.
If your skin is sensitive, get the clinic to do a test shot first. My clinic just did a couple zaps under my chin, testing two different lasers - in case there was some unexpected consequences, those spots wouldn't be disfiguring. When they cleared up, I came back 3 days later to do the whole face.
I heard people recommend starting HRT before laser for the simple economic reason that you'll have less lasering to do, because the hormones will have reduced your hair density / thickness.
Also, yeah, if you're under 18 and cost is a factor, this will suck. Multiple treatments are needed, no question. Those of us that with fierce 'adult' shadows need like 10+ treatments. Talk to other trans* people in your city to get a recommendation on an effective clinic. Some laser places are bad, I hear about people going over and over with little effect - just a money pit.