The influence of the Kalevala on Tolkien is certainly never to be underestimated, but I'm not sure Aino's story fits Goldberry very well.
To begin with, Aino at first is not a water-creature, or even associated with water (unlike her suitor, Väinämöinen himself, whom we first meet floating on the primeval waters in the beginning of the epos, and one of whose typical epithets translates as something like
water-dweller) but only becomes so after drowning herself in order to escape a forced marriage with him (which she may be about to do on the right panel of Gallén-Kallelas triptych).
Second, their first first meeting didn't take place by the riverside but in the forest (as we see on the left panel), and it's not she who tries to catch him but he who tries to seduce her.
Finally, when she allows herself to be caught by him, meaning to marry him after all (as we may assume, or rather hope, Goldberry did) she comes in the shape of a fish and he blows it by trying to gut her instead of taking her home as his wife, so she flees again after revealing her identity (middle panel). Fortunately Tom and Goldberry had a happier ending. If you look at Gallén-Kallela's painting in isolation, it could be taken as an illustration of Tom catching Goldberry, but that's not the story it tells.
I rather see Goldberry as descended from the nixies and water-nymphs, the undines and melusines of European folk mythology, which inspired
Arvegil145's
Ailinóne and her like. One of those was the tragical heroine of Friedrich de la Motte-Fouqué's novella
Undine, telling the story of another River-daugher (who, by the way, has an uncle named Kühleborn - does that remind us of anything?). While Fouqué's Undine is unlike Goldberry in a lot of ways (she marries a human knight in order to acquire a soul, which as an elemental she traditionally lacks, prefiguring Andersen's
Little Mermaid), a common element is a dangerous spooky forest that her parental river flows through.
Priya Seth, in an (at least initially) less-far-fetched-than-usual
blog post, makes a case for Goldberry being inspired by Arthur Rackham's illustrations for an English edition of
Undine, of which she reproduces several that, I must admit, look indeed quite Goldberry-ish to me (especially
this). There is, however, no evidence that Tolkien was familiar with either Fouqué's story or Rackham's illustrations, so all this has to remain speculation.
(Fouqué himself is largely forgotten today even in Germany, unjustly IMO. Apart from
Undine, which was quite famous in its day, he wrote several lengthy prose romances set either in Germanic antiquity or an idealised Middle Ages and often incorporating supernatural elements, which first plowed the field that later authors like William Morris and Tolkien himself cultivated. He also was the first to translate an Icelandic saga into contemporary German.)