By definition, the reason photo sharing sites exist in the first place is to bring photos and viewers together in the same place. If that site is a commercial site, then more photos and more viewers tends to yield more of whatever it is that site is monetizing (ads, memberships, etc.). So if it's a commercial site, and your photos are attracting any views at all, then your photos are being used for commercial purposes.
Intuitively, it might seem that you could get closer to your objective if you can find a not-for-profit photo-sharing site, but these guys (if they exist) have bills to pay, too, even if they're not making a profit, and you could consider efforts to that end to be "commercial" as well. Since "commercial purposes" is broad enough to include ads running alongside your photos, for example, which ties directly to dpollitt's point -- if you want complete control and freedom from (someone else's) commercial activities, you're going to have to pay the bill.
Given that you're ok paying for service, many paid photo galleries will let you password-protect albums or sections. Again, they're able to do this mainly because they don't need to drive lots of eyeballs through their site to make money; once you've paid for the service, they don't care whether anyone ever sees any of your photos.
Finally, for the ultimate in control, you can obviously self-host your photos. For lots of people, the time and energy required to do this well just isn't worth the tiny amount of control they'd have to give up in order to use an existing paid service.