Is it normal for the skin around the ink on my new tattoo to be slightly pink/red?

I just got a pretty big rib/side piece last thursday. I went to a well-known, professional shop, followed my artist's instructions meticulously, and have not let any clothing or anything irritate it AT ALL. I got the outline of california all down my side with the california bear in solid black in the middle, and am shading the whole thing in with the Rasta colors. So far, I have the outline, the bear filled in, and the red coloring done. I am supposed to go back tomorrow to finish the colors, is that too soon? I mean, I am fine with the pain, I just don't want to mess any other part of the tat up, even though he will not be going over any of the other parts.