my heart's deepest yearnings

Here "my heart" refers to the writer. It may be helpful to state that the writer desires good health. AT: "My strongest desires" or "that I desire you to heal me" (See: rc://en/ta/man/translate/figs-synecdoche and rc://en/ta/man/translate/figs-explicit)

my groanings are not hidden from you

This can be stated in active form. AT: "you are able to see all my moans of sorrow" (See: rc://en/ta/man/translate/figs-activepassive)

This idiom means his heart beats intensely. AT: "My heart beats loudly" (See: rc://en/ta/man/translate/figs-idiom)

"I become very weak"

"I can no longer see well"