Complained, having desire to be laid up? (7)

'complained' is the definition.
(bitching is a kind of complaining)

'desire to be laid up?' is the wordplay.
I cannot really see how this works, but
'desire' could be 'itch' (itch is a kind of desire) and 'itch' is found in the answer.
'be' is within the answer.
A single letter 'd' remains which might be clued in a way I don't understand.
This may be the basis of the clue (or it may be nonsense).

'having' acts as a link.

Can you help me to learn more?