Shin splints could be a passing phase. Two weeks after I started running track in high school, I got terrible shin splints. They lasted somewhere between a week or two. I'd say take it easy on yourself, but don't give up completely. You are switching from not regularly stressing those muscles, to regularly pushing them to the point you are short of breath and your blood-oxygen levels drop.

When your muscles aren't receiving enough oxygen from the bloodstream, they start to produce it themselves through a chemical process which produces lactic acid. This lactic acid causes soreness, and combined with the wear on your muscle tissue from exercise (what causes them to grow in the first place) it can also lead to swelling. The growing/swelling muscles will shift and this shifting can cause them to pull on your tendons from a slightly different angle (and with more strength) leading to your tendons becoming stressed and healed over in a similar process.

The whole thing hurts and it can take a few weeks to go through.

Of course, there could also be something else going on.