The description as "black or dark green" makes me think this is a leafy herb, rather than a darker brown spice. Many dried herbs start out a dull green when they go into the sauce, but after cooking for a while they darken and become dark green or nearly black.
I assume you've already considered and rejected basil and oregano, which are the most commonly used herbs in spaghetti sauce. Both tend to have fairly flat pieces of leaf, which are usually approximately square or circular, or at least not very much longer in one dimension than another.
Other, less commonly used herbs in spaghetti sauce include:
Marjoram looks a lot like oregano; the pieces are usually flat and round, so it's not a great candidate. But if you have a poor quality batch of marjoram with lots of stems in it, those could definitely get caught in your gums. Or if your mom put a lot of marjoram in her sauce, there might end up being a noticeable quantity of stems. It has a fairly mild flavor, so you could get away with a pretty large amount of it without overpowering the other flavors of the sauce.
Tarragon tends to come in pieces that are longer than they are wide, but usually still flat. It looks a bit like dried grass clippings, if the grass blades dried flat, without curling at the edges. But the edges could certainly curl in on themselves while cooking, which would give you more of a needle-like shape.
Thyme leaves are pretty close to round when fresh, but once dry they do become rather skinny and pointy. I often notice them as a slightly annoying texture in finished dishes. They could definitely get stuck in your gums. They tend to be a fairly light green in color, but maybe they would darken when cooked in tomato sauce, which is both acidic and quite dark in color.
Rosemary leaves look a lot like pine needles, but they also tend to be thicker that what I would expect to get caught in the gums. The end of the leaf that was attached to the stem is much pointier than the tip of the leaf, so it could be the stem end pieces that got stuck your gums. It's not a very common addition to spaghetti sauce so it might be something you overlooked. A spaghetti sauce with rosemary in it has a distinctly different taste from a "normal" spaghetti sauce seasoned with just oregano and basil, but if you add only a very small amount it's difficult to tell that the different flavor is rosemary. Certainly rosemary by itself has a more herby and aromatic smell than the final sauce, so if you haven't tried adding it to a sauce you should try that.
Since memory is rather malleable, it's possible you're combining the memory of several different herbs and spices. You might be remembering the smell or flavor of one herb/spice, but that's not actually the one that got caught in your gums. If that's the case it will be very challenging to narrow down. But you can expand your search parameters, eg, maybe the spice you remember wasn't actually green. If that's the case, consider long skinny seeds, like cumin, fennel or anise seed.
If you're remembering the smell/flavor of multiple herbs, you can test for that by sniffing two different jars of herbs at the same time; just hold them next to each other and inhale while moving them back and forth under your nose.