I would expect chafing on any 15 mile ride wearing cotton underwear. As mentioned above, cotton REALLY soaks up sweat and keeps it close.

I don't get the pads. Pre-synthetic pads, people rode wool shorts with thin chamois inside and hard saddles. No padding. Now, it seems as if the thicker pads are sold as 'designed' for longer rides, so designers seem to think thicker pads are more comfortable than thinner ones. It doesn't make sense, unless you take Steve Hogg's approach of padding in shorts/no padding on saddle. In fact it may not make sense at all, since ill-fitting thick pads can bunch up and cause chafing. Besides, the pads make it much harder to find shorts that fit, IMO and IME. The Aerotech Pro shorts have a nice, a thin pad but also have zigzag stitching right where I chafe.

I've tried Gold Bond's anti-chafing stick, and I chafed badly. There's a product called 'Unpetroleum Jelly' that seems to work well for me for rides up to 30-35 miles. I've stayed away from 'chamois' creams because most of them have petroleum jelly or mineral oil in them, and apparently pet jelly can clog pores and is hard to get out of clothes. The Unpet Jelly has a disgusting feel, though, and the tube is unwieldy, but it's all vegetable oils.

I have a lot of faith in detergent, and I have no problem wearing bike shorts without underwear. I wouldn't buy used shorts, though.

Amazon and ebay have very cheap shorts for sale. I don't know their quality, though, and I don't know if the fabrics wick moisture away. May be worth a try - just don't condemn all shorts if a pair of the cheapest doesn't help. Remember, it comes from the same people who put melamine in toothpaste and dog food, IIRC.