Cycling shorts: comfort vs bacteria / fungus?
Normal detergent should be enough even with cold water. I do have sports wash but don't use it every time. Getting stuff properly dry (ideally not machined-dried if you want it to last) is crucial though, and keeping it dry for a while seems to help too. Some sports fabrics can feel dry when they're not completely.  Washing stuff out in the shower is a bit of a last resort - OK when touring but not really enough, and hard to get the pads dry in a reasonable timescale.  I'd rather wait a day until I've got enough stuff to fill the machine.

I didn't bother with padded shorts until I was doing 70km pushing hard, and now up to about 4 hours saddle time even cheap foam-padded ones are adequate.   You seem to be in a similar position, so you could try buying another cheap pair or two, and always thoroughly (machine) washing them and thoroughly drying them.  Store your existing shorts thoroughly washed and dried. If you start pushing the distance further you might find you need (gel) padding after all.