Wax lyrical
— To talk in a highly enthusiastic and effusive way (i.e, to wax poetic).
— “He waxed lyrical about his splendid and amazing mentor-cum-muse.”
Wax and wane
— To undergo alternate increases and decreases.
— “The ebb and flow of the ocean tides wax and wane but my love for you stays at a constant fever pitch.”
In terms of waxing poetically these other words come to mind:
Histrionics
— Melodramatic behaviour designed to attract attention.
— “By now, she was accustomed to to his hysterical histrionics.”
Verbose
— Using more words than are needed.
— “It is said that much academic language is obscure and verbose.”
Melodramatic
— Characteristic of melodrama, especially in being exaggerated or overemotional.
— “Dr Josē flung the door open with a melodramatic flourish.”
Exaggerate
— To represent (something) as being larger, better, or worse than it really is.
Drama queen
noun (informal)
— A person who habitually responds to situations in a melodramatic way.
p.s.
Why not see these posts too:
— ‘Poetic license’
— ‘Poetic justice’
Anna Bidoonism 