So I tried this command:
/testfor @e[x=445,y=88,z=216,r=3][type=Item] {Item:{id:minecraft:egg}
But it did the "invalid entity UUID" error and didn't work.
You closed the selector's parameters and opened them again, breaking selector syntax. You need to include all parameters within the same set of square brackets. You've also not completely closed the NBT data, just missing a final closing curly bracket. Fixed:
/testfor @e[x=445,y=88,z=216,r=3,type=Item] {Item:{id:"minecraft:egg"}}