First yes thats what called a pinch flat, 80 psi isn't that much for a road tire of that size but pressure also depends on weight, that said normal pressure is normally around 90 -110 for most people I'd say for your weight I'd most likely run min. 100 psi and go up to 110 maybe.
As far as the soft spots you are talking about, it actually sounds like maybe you have the tube twisted inside and that's what the soft spots are remove tire and check tube make sure you have a little air in the tube when installing to keep shape.