Miss Bates said in Ch. 19 that Jane had a lingering cold (since 7 November) and that agrees with the Campbell’s opinions:

She had never been quite well since the time of their daughter's marriage; and till she should have completely recovered her usual strength, they must forbid her engaging in duties, which, so far from being compatible with a weakened frame and varying spirits… (20)

Jane’s visit to Hartfield is in Ch. 20 but I could not find a mention that she was unwell during the visit. People beyond her aunt and grandmother do seem to fear for Jane’s health:

"it occurred to me [Mrs. Weston] how very sad it would be to have Jane Fairfax walking home again, late at night, and cold as the nights are now. And as I looked at her, though I never saw her appear to more advantage, it struck me that she was heated, and would therefore be particularly liable to take cold. Poor girl! (26)

"That fellow," said he [Mr. Knightley], indignantly, "thinks of nothing but showing off his own voice. This must not be." And touching Miss Bates, who at that moment passed near "Miss Bates, are you mad, to let your niece sing herself hoarse in this manner? Go, and interfere. They have no mercy on her." (26)

Mrs. Weston’s fear Jane might catch cold walking home suggests she is not unwell at the Campbell’s party either. The next day Miss Bates confirms Jane survived the night intact: “Jane caught no cold last night” (27). Mr. Knightley may have troubled his carriage for Jane and Miss Bates to and from the party on account of her health. It seems their worry in based in reason; Jane’s health is delicate:

Her height was pretty, just such as almost everybody would think tall, and nobody could think very tall; her figure particularly graceful; her size a most becoming medium, between fat and thin, though a slight appearance of ill-health seemed to point out the likeliest evil of the two. (20)

As to the pretence of trying her native air, I look upon that as a mere excuse. In the summer it might have passed; but what can any body's native air do for them in the months of January, February, and March? Good fires and carriages would be much more to the purpose in most cases of delicate health, and I dare say in her's.” (26)

Jane has a pale complexion but Emma will not “allow it to have a sickly hue in general” (24). If Miss Bates is not exaggerating Jane may suffer from a lack of appetite:

The aunt was as tiresome as ever; more tiresome, because anxiety for her health was now added to admiration of her powers; and they had to listen to the description of exactly how little bread and butter she ate for breakfast, and how small a slice of mutton for dinner… (20)

Only three of us -- besides dear Jane at present -- and she really eats nothing -- makes such a shocking breakfast, you would be quite frightened if you saw it. …But about the middle of the day she gets hungry, and there is nothing she likes so well as these baked apples, and they are extremely wholesome… (27)