Getting back ache occasionally, like getting a cold, is entirely normal. About 30% of the UK population reports a bout every year. If you don't remember sustaining a physical injury, there's probably no tissue damage, as that would usually only happen with a significant degree of force.
It's useful to understand that acute back ache is most commonly a case of muscle fatigue*. Maybe you've been carrying heavy bags or over-done it at the gym; as a result, your brain perceives that prolonged muscle-loading behaviour as a mid-term threat and reacts be setting off a cautionary muscle-guarding pain designed to prevent you repeating what could eventually cause some damage.
The best solution for muscle-guarding pain is normal activity and taking a break from the activity which caused it. Not sure exactly what the cause was? Your body will let you know when you're doing something similar by hurting - so just avoid that, but do not forgo other activities which don't hurt, in fact, make a conscious effort to keep moving around!
Many people prefer not to take pain killers, but with this type of pain, they can actually be very helpful. They won't 'cloak' pain to the point you'd be able to damage yourself, but they will dampen that pain-receptor response enough for you to move around more freely and remind your brain that there is no actual tissue damage.
The majority of muscle-guarding back aches resolve completely within 4 or 5 days; and with regular activity, you should see significant improvement within just a couple of days.
Rather than catastrophizing about the possibility of long-term pain and your lack of mobility, reflect on what caused the issue; were you tired and less able to maintain correct posture when exercising? Were you over-reaching rather than moving your whole body to do a task? Whatever it was, it helps to understand what over-loaded your muscles and caused your body to respond with this protective pain. Finally, (you can probably guess what I'm going to say next!) massage therapy can help alleviate this type of pain. Ask your therapist what they would recommend.
*If something's impacted your back with force or if you've got other symptoms (eg numbness or pain spreading to your limbs), if your pain is constant in all positions rather than triggered by certain movements, or if it wakes you at night regularly, get yourself medically checked out. That is not the type of back pain I'm talking about here.