Agree with Laura. The leaves on your plant all look spoon-shaped, both surface leaves and submersed leaves. C.heterophylla has spoon-shaped surface leaves, but the submersed leaves of het I've seen are always straight, never spoon-shaped.
I'm having a few problems, and I'll explain why I agree it obviously can't be the usual C. heterophylla (
pictured here), yet I'm having very serious doubts it's C. stagnalis (
pictured here). In fact the best fit, as I'll explain, appears to be Callitriche heterophylla Pursh ssp. heterophylla, "twoheaded water-starwort". In fact the USDA site list a county with 20 miles of here for this particular "Pursh". Even closer with fewer geographical constraints than listed counties containing C. stagnalis.
Before going through these it should be noted that upon collecting these I packed the in that muddy container pictured. Then, with a little rinsing, the photo with the tadpoles shows the specimen fully submerged. The tops, which normally stuck out of the water, is now randomly mixed and submersed. Now let's compare these species.
Callitriche heterophylla:
The usual variety it appears my collection is being compared to is obviously distinctly different, as
seen in this photo, and attested to by key features and knowledgeable people here. So let's compare C. stagnalis and C. heterophylla Pursh ssp. heterophylla.
Callitriche stagnalis:
This has a general morphology quiet similar to my specimen, but note
this photo here. This photo indicates veins even more pronounced than the standard C. heterophylla above, while the veins of my specimen appear even less pronounced. The floating leaves appear far more compact and fibrous than my specimen seemed to exhibit. So let's just go with unconfirmed but likely status.
Callitriche heterophylla Pursh ssp. heterophylla:
Now
compare this photo. Here we have less compact, less fibrous, and the same leaf characteristics as my specimen. If you look at the tops in my specimen, primarily in the initial packing container, you will also notice the stem length on the leafs became much less pronounced, sometimes close to round while maintaining the same general shape, much that the above picture. This picture also indicates a less fibrous leaf. This site mentions a similarity with C. plaustris, but plaustris does not occur withing two states of here. In fact, based on these comparisons, this species appears to be a stronger match than C. stagnalis.
Furthermore, the UK identification site, used in the initial comparison say: "Identification to species level is beyond the scope of this site. Many botanists simply record the aggregate, as I do."
Geography:
Although there is a county, in the next state up within 50 miles northeast of here (as the crow flies) containing C. stagnalis, there are extensive geographical barriers. A huge series of ridges and, even going against the current, several hundred miles of river to get any kind of river transport. The prevailing wind tends to be northeast, so any wind transport more likely require a source in mid to southern Alabama. For "pursh" ssp. heterophylla the USDA list a source in a nearby county within 13 miles by road, with no geographical barriers whatsoever.
I think the only way to resolve this is to get samples of the flowers and fruit.