Will the use of coal tar 2% shampoo after Scalp Micropigmentation cause any damage or fade it? My doctor didn't know

Hi there, I have recently done an SMP after 2 failed FUEs, but I at the same time have quite a bit of flaking and dry scalp and eyebrows. I visited a dermatologist, and we tried with Nizoral, Elocon (corticosteroids) but nothing helped and my skin keeps flaking with some red spots here and there. The doctor now suggested 2% Coal Tar shampoo, so I was wondering whether that would damage or fade my SMP? My doctor didnt really know, so I hope I can get some help here. Many thanks in advance!