i dont know if it's just me but...
whenever i do back squats, the day or 2 after my lower back is also sore as if i was doing DL.
i usually go heavy. i know there is some core power involved with back squats but is my lower back supposed to be sore too?
Don't know if you googled for help or got an answer yet but here are some possible reasons your lower back feels this way:
1)your form could be off when going down on the squat. If you do ATG squats, as everybody should for maximum strength gains, you could be rounding your back when at the whole.
2)hip flexor might need proper warmup and mobility
3)you're not activating you're glutes(this is probably the reason why you feel so sore after. I'm confident this might be the problem from first hand experience)
When you're glutes don't activate, all the load is carried by your lower back. You should youtube some buttox muscle activation exercises or learn to ATG squats as you're glutes will surely activate when you get in the hole.
I suggest you also google this problem and you'll find a BB thread explaining this and with videos attached.
I noticed a huge difference in my squat after I started to activate my glutes. My lower back didnt feel sore like before. Now, I'm a new man.
Film yourself for a squat form check.