“Furball” and “being sick” are two different things.
Cats naturally ingest hair as they groom themselves, as you’ll know yourself if you’ve ever had the pleasure of licking anything furry for a period of time. Accumulated hair forms a ball (or more accurately, a sausage) which the moggie then coughs up.
So if Tiddles has left you a hairy sausage, it’s perfectly normal behaviour. OTOH, if it looks like someone dropped a month-old Lancashire Hotpot then I’d hazard it’s more likely to be a reaction to the chicken. Probably still not a cause for concern though, unless she’s sick continually or you see any other changes in her behaviour.
Of note though, cats are very good at hiding when they’re ill, it’s some survival instinct or other.