You can have a reaction to the influenza vaccine
and as there are many excipients in the vaccines, it is best that you see a specialist and explain the reaction you had.
People with severe egg allergy
react to the flu jab as the virus is cultured in egg and studies using vaccines from different manufacturers show significant variation in the ovalbumin content in them.
Try and taper the prednisolone
over the next few weeks and stop and start on antihistamines now.
The exact brand and leaflet together with the list of excipients will be required when you see your Allergist.