Are Daenerys dragons the only dragons in the seven kingdoms? [closed]

This has been a repeated plot point of the series (and books) every since the beginning. Dragons are believed to be extinct for about 250 to 300 years.

Dragon eggs have still been around (though they are incredibly rare). However, since no one has so far been able to have the eggs hatch (until Danaerys), the eggs are believed to be nothing but a souvenir.

The story starts at a time of relative peace (with Robert Baratheon on the throne). It has been many generations since the last dragon was seen. The same is true of white walkers and even magic in general (for most people).

It has been long enough that people have started believing that white walkers are a myth, and have never really existed.

However, the Long Night (the big war between humans and white walkers) was over a thousand years ago. Comparatively, the dragons have not been extinct for long enough that people doubt their existence. It has been between 250-300 years that dragons were last seen, as Aegon the Conqueror (who united Westeros and started the Targaryen dynasty that was only overthrown by Robert Baratheon's rebellion some 20 years before the story begins) used dragons to conquer Westeros 300 years ago.

As addressed in S07E01 (not a real spoiler), the maesters have tasked themselves with keeping the history books of Westeros.
Especially since Targaryens still ruled Westeros less than a generation ago; it stands to reason that both the maesters and the Targaryens have kept the memory of dragons alive. It is the sigil of House Targaryen, after all.

The Targaryen dragons were all but killed in a war that broke out between the Targaryens themselves (the name of this war currently eludes me). It wasn't long before the last dragon was reported to die, and no dragons have been seen since.

edit I feel I may have misstated here. The war between Targaryens did not kill all the dragons, but a considerable amount of them (> 66%) died during the war. The remaining dragons died off later, in relatively minor and unimporant ways. Maester Aemon (Targaryen) mentions that the last few dragons were weak and small, due to being raised in a castle, not their natural environment.

However, it is my interpretation that those dragons were not (just) weak because of the castle environment (look at how much Danaerys' dragons have grown in the dungeons); but that this somehow ties in to the presence of magic. In aCoK, it is mentioned that "the glass candles are burning again", which is an indication of the resurgence of magic.

This seems to coincide nicely with the dragon births, re-emergence of white walkers, the Fire Lord's miracles, etc. This also indirectly means that magic must have waned at some point in the past (otherwise it couldn't be a resurgence). As dragons are magical creatures, they may have been more prone to extinction after the magic "died down" (or whatever you want to call it), which may have expressed itself as dragons being weak and small as they have no magic to feed off (and people wrongly attributed it to the castle environment due to coinciding events).

If Danaerys hadn't hatched the dragon eggs, and another 700 years would have gone by without any dragons, they would presumably have been assumed to be a myth, as much as the white walkers currently are.

Maybe slightly in support of your hopes of seeing more dragons:

I'm not sure if the books have confirmed/denied this; but it is maybe possible for the white walkers to bring dead dragons back to life. We've seen them do it for humans, giants and horses.
Unless the books have already confirmed it to be impossible; it should be possible to resurrect dragons.