This type of redness is often a form of cellulitis (literally translated as an inflammation of the cells), a catch-all sign of infection or other irritation. Red lines are signs that the infection is spreading. In this example, submitted by a reader, this was thought to be a spider bite.
While theoretically, spider bites can be a route for infection, there is very little evidence to support the theory. There's just so much that can cause infection that without seeing a spider in the act of biting, we can't really blame the spider.
There's not much you can do at home on your own for cellulitis. You'll have to go to a doctor.
Any opinions expressed here are for educational purposes only and are not intended for diagnosis.