It depends on the time of day… we have gone and found shade under the pergola at the tables in the corners, or under roof near the restrooms.
How about bringing a pretty parasol? I bought some large, colorful asian style paper ones (Pier One) that were quite fun, I brought one along when one of our fairest daughters was visiting. She got a lot of smiles, waves and
I do wear a baseball hat in the pool and my sunglasses, even for water aerobics…. and use waterproof sunblock.
I know there are now lightweight, long sleeved, UV protectant tee shirts that are sold as swimwear. Land's End (online) is one place to get them reasonably.
Good Luck