Your instructions on unwrapping it when you got home are different than any instructions I've ever received. Normally I leave it covered overnight before unwrapping and cleaning it.
Plasma and ink discharge the 1st night or two is quite normal.
Redness, soreness and some heat are normal for any skin abrasion, including results from tattooing - but if it's hot and truly painful then infection is a possibility.
What you're describing above sounds pretty normal. Your tattooist should be open to taking a look at it, too.