Yes, I had the same experience, it's so frustrating and uncomfortable! It took a lot of trial and error to see what kinds of underwear worked for me. I had a few random hits and misses from various brands, but the kind I kept going back to was this Maidenform cotton bikini. It comes in 3-packs of varying colors and patterns, and I think you can still find them at Kohl's and Ross although they aren't on the Maidenform website anymore. It looks awful on the model here, they look better in person and on my non-model body imo! But at least you can see from the model photo that it has a wide crotch that allows for a little pocket for the extra lip volume, and I like that the elastic around the leg holes is thin: I think it helps create a tighter barrier at your leg-crotch-junction so that a lip won't as easily slip out of and get pinched. Keeps everything contained.
If these aren't cute and fun enough then I understand, but maybe at least the tip for looking for wide crotches with thin leg elastic can be something to watch out for when shopping in cuter brands!