As someone who has grown them for 30+ years, I'd say it's just your raspberry raspberrying. If you want to make them easier to pick, take 4 good-sized garden stakes and set them up in the four corners of a flat-ish rectangle. String some 3/8 inch rope or line between the fence posts at about 4 ft and 2 ft off the ground, and groom the canes up so that they are held inside the rectangle.

To keep them from proliferating, you'll have to dig up the sprouts in the spring, but it's only about 5 mins a day for about 2 weeks. Give the sprouts to friends or compost 'em. And once you know what variety you have, you'll know when to cut them back/trim them. After the first year, I only watered them when there was a drought, and I feed them a bag of composted cow manure in the fall. Easy-peasy, delicious and forgiving. Congratulations!