Green’s Dictionary of Slang

wrapped adj.

[abbr. SE wrapped up in]
[1960s+] (orig. Aus./US campus)

1. besotted with, infatuated by, in love with.

2. fascinated by, enthused with.

3. delighted; overwhelmed with pleasure.

4. see wrapped up

In phrases

wrapped up (adj.)

1. [1900s–40s] (US) aware, ‘in tune’, sophisticated.

2. [1910s+] affected, in love with.

3. [1940s+] (also wrapped) sorted out.