Jilly, I would ask the tech what type of laser and the settings they are using. If it’s a good reputable place, they ought not be evasive about this information. If this is a true laser, the request to have several days of growth is not logical. A laser targets dark pigment, so you actually WANT to shave beforehand so that the energy is focused on the root, it’s the root you want killed!
I have had two Diode laser treatments so far, spaced 6 weeks apart, on my chin and upper lip. The pattern has been that the hair starts to shed about 9 days post treatment. I notice the shedding even though I continue to shave the area mostly by tugging on these hairs with a tweezers. If they resist, I leave them alone, but usually they slide right out. I also use an exfoliating cream to help the process along–once any soreness has subsided.
It sounds like you have not experienced any shedding at all, which you should have had some even after the first treatment. I would definately start quizzing your tech before you spend another dime.