Is It Possible to Treat Post Inflammatory Hyperpigmentation During Laser Tattoo Removal?

I have been receiving laser tattoo removal for a black densely-inked tattoo on my forearm. My tattoo is fading (not completely yet, but getting there). However, I am experiencing permanent redness where the tattoo ink was. It seems to be post inflammatory hyperpigmentation. I have spaced my laser sessions apart so as to prevent this. I have also used sunscreen. I ordered silicone sheets. Should I/Can I use hydroquinone or hydroxy acids in between laser treatments? If so, what brands? Thanks!