I am looking for a noun that is a synonym for "scared of being made fun of".
The only phrase that I can come up with other than "social anxiety", which Peter has already mentioned, is "fear of humiliation".
In her book Fear and Other Uninvited Guests, psychologist Harriet Lerner points out that of all the forces that shape human behavior, fear of humiliation is among the most powerful. The most common fear is not of illness or accident, but public speaking; soldiers will march into certain doom rather than be branded cowards. (Source)