Broken capillary and PIH. What is the best treatment? IPL?

For many decades already, starting long before the advent of expensive bells and whistles lasers, and the very heavy marketing for the use of these expensive devices, small, "broken" blood vessels were treated with an under a second application of simple, safe, effective and inexpensive electrodessication, which typically yields the desired effect immediately. I personally give my patients a mirror to watch as the vessels seem to magically disappear. So, don't fall prey to the intense advertising and marketing for this or that expensive laser. As to the under eye darkening, this may be post inflammatory hyperpigmentation due to the irritation caused by the benzoyl peroxide. If so, there are prescription creams that can be applied to hasten the fading. Make sure to consult with a board certified cosmetic dermatologist who can help you with both problems. And best of luck.