"I am a little busy this month."
Adverbs are like adjectives for verbs. They change the meaning of the verb (eg. quickly, slowly): 忙しい busy is an adjective: I worked at my busy office. (<- This sentence implies the office was busy.) 忙しく Adverb of busy is busily: I busily worked at my office. (<- This sentence implies that "I" was busy.)
(I'm still an amateur at Japanese, so don't ask me to use those in a sentence, haha.)
The negative form of the adjective is adverb + Nonexistence.
To make an adjective negative you must attach it to the negative verb of existence "arimasen" formal or "nai" informal.
You use the adverb form to describe the state of non-existence. "Is busy" in negative literally becomes "does not busily exist"
So 忙しい Busy → 忙しく Busily → 忙しくない Not busy(informal) / 忙しくありません Not busy (formal)
just for reference, if someone else reads this in the future. Yeah, they are kinda weird together but ちょっと is already too common and sometimes appears like this. There is also different levels of politeness in Japanese, in a business setting you would probably use 少し忙しいです though.