Crycket, have you Googled "sun protection garments"? There are all kinds of blouses, shirts, pants, hats, etc., that keep the sun off of you, and help keep you cool. They even look OK.
A friend has severe sun allergy, but she's an avid gardener. She has found some success with these garments, and a big hat.
A nice, lacy sweater would probably still let the sun get to your skin.