I'd definitely try some sort of lube before you puzzle out any other factors... it's probably the simplest thing to try, and if that works, then you're good). Chamois Butt'r or similar is relatively cheap, compared to buying good shorts or another saddle.

Since you're doing fairly short rides... my second thought would be that it's your saddle, not the shorts. I could do 12 miles without bike shorts on without a problem... but before I had the "right" saddle for me, I was in agony within just a few miles.

If you can figure out if you're truly dealing with chafing (from rubbing and lack of lube) or it's actually your lady parts getting smashed, that could be helpful.