to be burdened with

• 杂事缠身

  be bogged down with tasks

• 琐事缠身

  be inundated with chores

• 琐事缠身，我不能来了。

  I'm so up to my ears with chores that I'm not able to come.

• 债务缠身

  be burdened with debts

• 长年重病缠身

  be afflicted with chronic illness