It sounds like you just need some more shorter rides to get used to the saddle.
The pad in bike shorts won't help very much. It's more to keep wrinkles on the shorts or stitching on the saddle from causing a sore spot. And to soak up sweat.
Back when I started riding, I sat on a scrap sheet of foam, maybe a half inch thick, on the first few rides. A terry cloth towel folded up might do the same thing.