Can you please elaborate on how you are adding hydrogen peroxide to sulphur dioxide? Are you bubbling sulphur dioxide through hydrogen peroxide?

I am adding a few drops (total volume = 150ul) to a glass of young red wine which means it has a lot of SO2 present.

SO2 is in form of sulfit (SO32- ) in aquous solution. With the hydrogen peroxyde it will be oxydised to sulfate (SO42- ). In wine one part of the SO2 is bonded to other molecules of wine. This combination can be irreversible (with aldehides) or reversible. When the free SO2 is decreased, the reversibly bonded form will be liberated. It is an equilibrium between the revresibly bonded and free forme.

Presuming you are adding peroxide to wine then the peroxide will rapidly react with the free SO2.  In wine SO2 is bound to a greater of lesser extent to compounds such as aldehydes, alpha keto acids, quinones, anthocyanins, some sugars ..... and what isn't is "free", that is available to act in other ways such as an antioxidant and anti-microbial agent.  That is not to say the some of the bound doesn't contribute to this activity for some binding is quite loose and reversible when the free SO2 is reduced in quantity.  The majority of the free is present, at wine pH, as HSO3-, not SO3=, not H2o.SO2 which are the minority forms.  The HSO3- is readily oxidised by H2O2 to H2SO4 which of course will exist as ions.  Excess peroxide will then oxidise phenols, and flavour/aroma compounds destroying the taste of the wine.  For an fuller explanation see the entry on sulfur dioxide at:

http://www.brsquared.org/wine/

Thanks for all your answers  - very helpful! Do either of you know if people who get red wine headaches are reacting to bound SO2 or free SO2?

I note you talk of adding it to young red wine "which means it has a lot of SO2 present."  I have to disagree unless you mean 15 mg/L is a lot.  Most red wine in my country at least, and as one who has bottled many thousands of litres of red wine, it is normal to bottle with about 20 to 25 mg/L free SO2 in reds, a little more is common in whites, Then within in a couple of months the free will have dropped by anything up to 10 mg/L depending on wine bottling technology and control over aspects such as dissolved oxygen.  Our body has enzymes capable of handling much more free SO2 than this.