Post-inflammatory Erythema (PIE) indicates redness, or dilated capillaries, as opposed to Post-inflammatory Hyperpigmentation (PIH), which is brown and implies melanin deposition in the skin. Hint: Pressing on the skin with a clear glass slide or similar will temporarily push the blood out of the capillaries, removing any PIE so that you can tell how much PIH is there! Almost everyone has a mixture of both.
Redness that acne leaves behind takes a long time to resolve (this can be 3 to 6 months after the blemish appeared). Any red discoloration will fade with time, and other treatments do not typically add a lot; however, medications that fight inflammation may reduce redness to a variable extent. Procedures such as vascular laser treatments may help, but the passage of time usually does the trick!
Acne can come back in the same spot because of local factors that increase susceptibility to breakout in a certain area of the face—such as sitting chin-in-hand while reading or working on your computer. Often, a pimple recurs in the exact same spot because there is still inflammation deeper in the skin, which makes the spot vulnerable to the usual acne influencers, such as hormones, stress, diet or local irritants.