We have a DD with allergies and only from my experience, I have found most reactions get better over time, not worse.(what i mean is that I haven't seen a rash keep growing over time if it's allergy. But that is not saying it doesn't happen). STrawberries do cause a rash for alot, and if there's egg in the custard it could be that. My DD has severe egg allergies. Her rash comes up very quickly (along with alot of other things) but does disappear. Of course all reactions can be different, but I'd look into the egg.
Also DD reacts to a pin***** of egg.
Hope the rash improves. If it is allergy, polaramine is good (oral liquid) or any antihistamine for baby (check wiht Doc first anyway, but I found the first time I rang an allergy line with a reaction they suggested this). Also a mild quarterzone cream. Sigmacourt is good applied sparingly xoxo

PS What about measles?