Does shaking carbonated water before use increase the carbonation

There are a couple of reasons why a wine would be slightly fizzy:

1. Maltreatment: wine which has been stored in a hot place will often be slight fizzy, as well as having a "sour cider" taste. This wine is ruined, throw it out.
2. Varietal: in addition to Champaigne/Prosecco/Cava,several other wine varietals are deliberately slightly fizzy, such as Lambrusco and some Vino Verde. They may not be labeled as fizzy because it's assumed you'd know from the varietal.

I'm going to have to contradict BaffledCook here: by the time a regular non-sweet wine is in the bottle, it should not have residual sugar or fizzyness, even if it's too young to drink. For standard wines, all sugar is converted in primary fermentation, and certainly none would make it through barrel-aging. So if you get a chardonnay or pinot grigio or merlot, and it's slightly fizzy, it's ruined and you should take it back to the market and exchange it.

EDIT: see discussion in comments.

SECOND EDIT: I went out and bought a 2011 white wine, and darned if BaffledCook isn't right. Very young, but otherwise good, wines can have a slight effervesence. So combine his answer and mine for 3 reasons why a wine would be slightly fizzy. Mind you, you shouldn't be drinking 2011 wines yet ... store them for a year ... but if you do, there it is.

The real issue, I think, is that you want to add the egg whites immediately before service, as they will begin deflating once they are whipped and mixed in.

So instead of holding the mix a certain period of time, instead you hold the mix until prior to service, and then fold in the whites, which should be freshly whipped.