Well, there aren't any "sulfites you put in wine to stop fermentation", so your doctor is obviously not aware of winemaking and ingredients. Sorbate is what is used at that point to inhibit fermentation. Perhaps she is sensitive to sorbate, or perhaps not, but sulfites don't stop wine fermentation.
Sulfites are naturally occurring, and routinely added as antioxidants, but dissipate quickly so are usually re-added at intervals and at bottling. You can leave those additions out but the wine will not last as long as with it. No big deal, but chemically they are IDENTICAL to the sulfite produced during fermentation, and home winemakers use tiny amounts compared to commercial winemakers. There would not be any discernable way to tell which sulfites are naturally occurring vs those that are added at racking to inhibit oxidation, and they do dissipate to a degree anyway so it's not like they would be there later on.
In any case, you don't have to add sulfites anyway so it doesn't matter. Wine will ferment until it's done, and if you are not sweetening it, there is no reason to add something like sorbate to stop fermentation. If you want to do a sweet wine, that would be an issue. Any sugar added would be likely to create bottle bombs if bottled without stabilizing before adding unfermented sugars.
Still there are some techniques like adding sugar at intervals so that the yeast is overwhelmed, resulting in a sweet wine when done. The issue with that is that you can have an 18% sweet rocket fuel for several years until it ages out.
Or, you could try bottle pasteurizing by bottling with crown caps and doing a hot water bath. It's iffy if it'll work, but it might be worth a shot if you want a sweet wine or cider but don't want to stabilize with sorbate.