What are alternatives to prednisolone for a toddler with a chesty cough?

Sorry to hear that your child has developed hives after an episode of viral illness. I agree with Dr Colin Theng that a viral infection is most likely the trigger for this episode and antihistamines such as cetirizine would be the mainstay of treatment. I would usually optimise the dose of antihistamines for good control. If the maximum dose is still not able to control your child's hives, then a course of prednisolone may need to be considered. These medicines will help to switch off the activity of mast cells which have gone into overdrive, causing the appearance of hives.

Croup is a viral infectious respiratory illness affecting mainly the voicebox, windpipe and sometimes the lungs. Many viruses can cause croup, including those responsible for the common cold and flu. Hence, the measure to prevent a croup are similar to that for a common cold. These include practising good hand hygiene (by washing your hands regularly), coughing and sneezing into a tissue or into the elbow, cleaning surfaces regularly, avoiding food/drink sharing and keeping your children's immunization up to date.