Hi Cocheze! I would definitely do some basal testing to see if that's what's happening. To me, it's always better if you can get that worked out since it will make a huge difference without you thinking too much about it. Of course, it can also change over time, so keep that in mind!
What my endo will have me do is fast the same time of day two or three times (assuming I start with a normal number) and test several times (I do on the hour for about 4-5 hrs), then I'll send him the numbers. Once you see the numbers, though, you can usually get an idea of what's happening! When you get that basal rate worked out, move on to the next basal setting.
Or if you don't have different basal rates set up for different times of the day, maybe that's something that could help.
Hope that's helpful! Unfortunately, our blood sugar is always a moving target! Let us know what you figure out!