Hi, Beka !
What you're experiencing is not unusual.
Most women tend to do a lot of AB work in hopes of getting that a flat stomach. Well, in their quest for that flat stomach, they tend to neglect their back muscles. Your back muscles are the complimentary muscles of your abdominal muscles. That means they support your AB muscles much in the same way your AB muscles support your back i.e. they compliment each other. So, if you've been neglecting your back muscles in favor of your ABs, it's not a surprize you had a sore back. You have weak back muscles.
So., your AB muscles are stronger than your back muscles. That creates a muscular imbalance. My suggestion would be to ADD exercises that also work your back muscles. Some good back exercises include push ups, bent over rows, single arm rows, flies, plank and side plank.
Don't just work your ABs, work your core muscles for the right muscular balance.