I had a similar problem: I wore jeans (I have to work) and they chafed my then-new tattoo, causing scabbing, and then discoloration.
While getting other work done with my artist, I asked him about it and he said to wait. Here we are a few years later, and the color has healed fine: there's no brownish red anymore where the scabs were. So a touch up isn't necessary at this point.
Now, the color falling out is a different issue, which will most likely need a touch up, and my tattoos are tebori, but the lesson is that allowing the body to work its magic over a longish period of time isn't an unreasonable or unheard of thing.