Thy = your (archaic form)
The rose is the symbol
Thou art sick = you are ill
The meaning could be construed in many ways. The rose is often a symbol of love, and the invisible worm is, to me, a sexual symbol. I think it's a bout someone losing her virginity outside the accepted norms, and becoming defiled as a consequence. Other people suggest that it might be about rape, but I am not convinced.