come down with sth [no passive] to get an illness that is not very serious: I think Iím coming down with flu.
to get or obtain sth: I seem to have picked up a terrible cold from somewhere. I picked up £30 in tips today.
come down with (an illness)
to begin to have or suffer from (an illness)
▪ She came down with [=contracted] measles.
▪ I think I may be coming down with [=getting, catching] a cold.
pick (something) up or pick up (something)
to become sick with (an illness) from someone or something
▪ I think I picked up [=caught] a cold from someone at work.
Student or Learner