Are you looking for an adjective or a noun? "Exaggerator" is a noun.
It is also totally a word, if not a formal one.
You can also call someone who exaggerates, a "hyperboliser/hyperbolizer".
The "-er" suffix creates nouns which refer to people, from verbs. It is a living suffix, which means you can add it to just about any English verb to create a noun which refers to a person. You won't always find these nouns in dictionaries and sometimes they are rather informal, but they are still valid.
eg: "Don't worry about Hawash; he's an exaggerator. He's fine."
If you're looking for adjectives to describe people who exaggerate, then you can say they are "melodramatic" or "theatrical".
eg. "Hawash is just being melodramatic. He's fine."
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As an aside, you should say, "looking for" not, "looking about".