I gulped and looked around fretfully for the exit

I gulped and looked around fretfully for the exit

Is there any phrasal verb here?

Notice that place (around) would come before mode (fretfully) before the prepositional phrase.

What about this rewording?

I gulped in fear and looked for the exit fretfully around (the manor)

This is what the Oxford Dict of Phrasal Verbs (ISBN 0194315426) says:

First: "phrasal verb" just means "a phrase that has a special (verb) meaning of its own, distinct from the meanings of each word."

"Look around" does have dictionary entries (Merriam-Webster, Cambridge, Collins). That suggests it can be a phrasal verb, and indeed Merriam-Webster's definition of "to search (for something)" seems to fit here. (But note, just because you find an entry for a particular phrase, doesn't mean it's being used that way. "Look up" is a phrasal verb in "look this word up in a dictionary" (where "look up" means "search for in a list") but not in "look up at the ceiling" (where it just means "look," plus "up").

The fact that the adverb "fretfully" doesn't interrupt "look" and "around" isn't a way of determining. It's certainly possible to interrupt like that, especially when the preposition itself takes an object ("look fretfully around the room"), but it's also common to keep the preposition close to the verb, even without any recognized phrasal verb. "Jump up" is not a phrasal verb, but "I jumped up hastily" is more likely than "I jumped hastily up."