In the 1960s, there was a well-known sketch comedy show on BBC television, starring Peter Cook and Dudley Moore, called Not Only... But Also. If you remember this title, you will have no problem with this particular parallel structure again. The only slight complication is whether to balance "not only" in the first clause with "but also" or simply with "also" in the second. In a short, simple sentence highlighting a contrast, a "but" should normally be included:
I was not only injured, but also insulted.
However, when the subject and verb are repeated in the second clause, the "but" should be omitted:
I was not only injured, I was also insulted.
The sentence in your question is of this type:
Not only was Jill very ill from lack of sleep, she was malnourished from a poor diet.
You could, if you wish, recast this sentence in such a way as to use "but also." There are several ways of doing this. For instance:
Jill was not only very ill from lack of sleep, but also malnourished from a poor diet.
However, it is not necessary to recast the beginning of the sentence in this way. The simplest amendment you can make is to include the word "also" in the second clause:
Not only was Jill very ill from lack of sleep, she was also malnourished from a poor diet.
This gives the sentence a sense of balance, which is the aim of parallelism.