The situation you are describing has a technical term (of course). It is called onycholysis. The fingernails may partially separate from the fingertips, which makes it difficult to keep dirt from accumulating under the nails. This is associated with the hyperthyroid state, and should improve one treatment is effective.
You can also sometimes see longitudinal “cracks” along the nails. The nails, when you are hyper, are growing too fast, and are more brittle. Just like what happens to our hair. Drat. This is the first time in my life that I’ve been able to “grow” nails, and they keep breaking off. Well, at least the breaks grow back quickly. : )