Is this expression current or old-fashioned?
The expression 'to make a .... of oneself' is both current and very common. Here are some examples:
I hope I don't make a fool of myself at the dance class.
John made a real idiot of himself when he got drunk last night.
The children often make nuisances of themselves on long car journeys.
'Making a pest of himself' isn't an especially common expression, but it fits into the above pattern. As you can see, it's generally negative things that we make of ourselves!