Could be as simple as the ground water/ water table being too high. If things start to improve with less rain, you might be good soon.
I'd suggest, for now, if you have the option, to adapt you washing machine to drain into your yard, or anywhere other than your septic system. probably not as easy to do with your dishwasher though. Check your drainage outside and make sure you don't have a problem near your drain field where water may accumulate.
I guess you should have your tank pumped, but it will fill back up pretty fast, and if your drain field is clogged, you'll be in the same mess. Make sure you have access to the distribution box after they pump the tank so you can observe the output of the tank once it fills back up.
I've tried a few things for clearing up a drain field, but the easiest that quite a few people report success with, and I have had limited success with, is putting about 8 pounds of disolved oxygenated bleach (OxyClean) into the distribution box, every two days or so for a week. It's supposed to feed oxygen to the bacteria in there to help it eat the sludge. Dollar General has a generic OxyClean for about 4 bucks for three pounds if I remember right, I believe Target has a generic too, for around the same price.
I need a new drain field, but have been putting it off, while getting by for now.
Good Luck, I know it sucks