"Care of him! -- Yes, I really believe Darcy does take care of him in those points where he most wants care. From something that he told me in our journey hither, I have reason to think Bingley very much indebted to him. But I ought to beg his pardon, for I have no right to suppose that Bingley was the person meant. It was all conjecture. ... It is a circumstance which Darcy, of course, would not wish to be generally known, because if it were to get round to the lady's family it would be an unpleasant thing."
Col. Fitzwilliam unknowingly let's the lady's closest family member know everything in regards to Darcy involvement in breaking up Jane and Bingley. And the unpleasant emotions (anger and indignation at Darcy) leads to physical illness.
Elizabeth made no answer, and walked on, her heart swelling with indignation.
There, shut into her own room, as soon as their visitor left them, she could think without interruption of all that she had heard.
The agitation and tears which the subject occasioned brought on a headache; and it grew so much worse towards the evening
So, there she is feeling ill from emotional upheaval of the afternoon and then Darcy walks in.