The true level of my single handed fighting is something like 37, yet the number it is showing is 15, and the numbers are red.

I went to a shrine and got a blessing: all ailments healed. I checked my stats and it shows no negative effects, and I am not wearing anything that I believe would cause any problems.

Where does this come from, and how do I get rid of it?

Same thing happened to me with archery. Went from 60 to 15. I couldn't figure out what to do about it so I just reloaded an hour old save from before the problem.

Hmm, remember in Oblivion when a stat was red it ment that something(disease, spell, ect) was making it worse. The weird thing is that the shrine should have fix it. Try reloading a save?

I had the same thing happen to me just inc the skill and it should turn back to normal
edit its a visual bug

What do you mean Inc the skill?

increase.