Bummer about your back pain. Short answer: Yes.
In my experience though, low back pain is caused more by inactive glutes and core muscles than it is by tight hip flexors. Hip mobility is also a potential cause but lets start with the former.
The psoas gets a lot of attention because it is literally attached to the spine so it makes sense to say that if it's tight, it's pulling on the spine and causing pain. We tend to blame sitting but when most people sit, they sit with a posteriorly tilted pelvis which basically means: Ya slouchin. sitting with "good" posture actually shortens and asks more of the hip flexors than "bad" posture because of the tension required to stay upright.
In general, you want to be aware of WHEN your back hurts. Is it after sitting for a long time?- Probably do some core activation.
Simply lay down on your back and bring your knees towards your chest until you feel your abs turn on. This is a reflexive activation that we are born with and happens automatically. Then, roll your tail bone up off the ground to get a little more, and breathe into your stomach. If you can't breathe, back it off a little bit. We don't need a ton of tension here. Our backs don't hurt because they're weak, they hurt because they're doing all the work.
Does it hurt more after standing?-probably look at glute activation. Because larger glutes are the evolutionary adaptation that allows us to stand upright. Ever seen a monkey's butt? Not a lot of junk in that trunk.
Just lay down on your back, squeeze your abs, press your feet into the ground and do a glute bridge. There are plenty of videos on youtube for this. if you still can't feel your glutes, Try foam rolling your inner thigh and calves and try again. Still nothing? Find someone who does Neurokinetic therapy and they'll help you turn them on. It'll blow your mind.
Hope this helps!