Tortle AC Shell Defense + Shield

I've been looking at making a Tortle Sorcerer, I'm wondering if Shell Defense stacks with using a shield. Since Shell Defense says that you are in your shell, I'm not sure if you can also hold a shield at the same time, Basically covering up your "arm hole" with your shield?

This would mean that I could have my natural AC of 17 + 4 (Shell Defense) + 2 (Shield) = 23. Which would be really nice, it already says you can gain the benefit from a shield, But it doesn't say anywhere whether you can use your shield while in your shell.