If you haven't been diligent about gravel cleaning, this is another possibility. Anything decaying in your tank is a possible source of NO3. Clean filter sponges, rinse media, vacuum gravel, etc. Sand is a definite suspect, while it's good at keeping wastes near the surface where the filter can get at it, it's equally good at keeping in anything that works its way down.
Water changes are great, and they'll get done along with gravel vacuuming. But in this case they're treating the symptom, not the cause. It's not magically appearing, so find out where it's coming from and attack that, if you can. If it's in the source water, you're outta luck, unless you want to start shilling out the big bucks for RO or DI water or for an RO unit.