Hi Kate, and welcome to TE! It's great that you're getting back on a bike! (And you're right--it's awesome stress relief.)

As to your saddle issues, I'll guess, but there are people far more knowledgeable than I who can chime in.

First off, if you've just gotten back on the bike, your sitbones are going to have to get used to the idea of being on the saddle. They'll hurt a little until you develop "butt calluses". The fact that only one hurts (or hurts more than the other) tells me that you're sitting only on one half of the saddle, probably because of the pain in other parts. Make sure the saddle is wide enough for your sitbones. Grab a tape measure (and maybe some play-dough). There are instructions in posts linked to in this thread to measure them. There are spots on the back of the saddle where your sitbones are supposed to go. If the saddle is too narrow, even if you're perched on it, your soft tissues end up supporting your weight.
If the saddle is wide enough, it may be adjusted wrong. Try tilting it down a little. An LBS or someone mechanically inclined should be able to tell you how. Just don't tilt it down so much that you slide off! Move it backward or forward a little and see if that helps, as well as up and down (again, just a little). Your girly bits may also be getting squished because you need a cutout. That thread I linked to earlier has a "chair test" to see if you might need a cut-out or pressure-relief channel.

Try E-bay, Craigslist or even check the For Sale section of this site for used saddles. They are so very personal and we often go through a few before finding "the one." Bear in mind, though, that you don't want a really padded one. Padding gets compressed and can cause even more pain!