Sounds like it "broke", as can happen with any dairy product. The protein in the kefir coagulated into the strings you are seeing. If you decide to try it again, try the highest fat kefir you can find, minimize acid in the dish, and incorporate the kefir at a relatively low temperature.
The dynamics of the Grain growth are not currently well understood, much less its formation. Some researchers attempted to create grains in laboratory, but failed.
There are over thirty or fourty strains of microbes in the kefir, and their ecological relationships are very complex. One could call the whole kefir culture an ecosystem of its own.
The grains grow either because the matrixes of existing grains entice the microbes to create more grain matrix, or because there are specialized microorganisms inside the grain that are responsible for creating more grain.
What is known is that the grains need Kefiran to grow, and Kefiran needs Alcohol in its synthesis. Commercial cultures of kefir often omit the alcohol-creating yeast for obvious reasons, so it too adds to the impossibility of getting Kefir grains from commercial kefir.
Either way, the fact is there grains do not come into being on their own. New grains are split from existing grains.
There is a small possibility that a kefir culture from grains that was strained could form new grains, but its not confirmed.
The commercial cultures are sold with around five to ten strains, much less than full blown kefir grains. They won't form grains, since the strains were hand-picked in lab by their function, and probably the grain-forming ones were left out.
Best Answer
If the taste is similar to yogurt, cheese, or sour milk as you describe then your kefir is likely good.
On the other hand, if it seems moldy or rancid, it is bad.
This site describes proper storage, shelf life and how to tell if it is bad.
And this site describes kefir gone bad if "f there is noticeable fuzzy mold growing on it, if there are pink or orange spots on it, or if it has turned pink or orange. Your body knows when it is bad, it should literally be revolting to you if you attempt to ingest it."