The correct option is
C There are plumbing problems not only in the kitchen but also in the bathroom.
The conjunction, 'Not only.. but also' is a correlative conjunction, which combines two grammatically equal items. This means that the words which follow both parts (i.e 'not only' as well as 'but also') should belong to the same parts of speech. Using different parts of the speech after 'not only' and 'but also' makes the sentence imbalanced and grammatically incorrect.
Option A: When a sentence begins with 'not only, it is followed by an auxiliary verb like 'did'/does'/'is' + subject. In this option, the sentence begins with 'Not Only'. However, this is not immediately followed by any auxiliary verb. Hence, this option is incorrect.
Option B: The phrase, 'not only' is followed by 'are', which is a verb. However, the phrase 'but also' is followed by 'in the bathroom', which is a prepositional phrase. Hence, this option is grammatically incorrect.
Option C: The phrase, 'not only' is followed by 'in the kitchen', which is a prepositional phrase. The phrase 'but also' is followed by 'in the bathroom, which is also a prepositional phrase. Hence, this option is grammatically correct.
Option D: In this sentence, the phrases 'not only' and 'but also' are used together, which is grammatically incorrect.