Well.. as usual with these questions we should separate two groups: One is The Vikings, the noble savages of pop culture, pop history, and 19th century romanticism. The bearded warriors whose exploits are chronicled in the Sagas, who believed in the elaborate mythology of the Eddas, who braved the oceans in their dragon ships while wearing their horned helmets. Tons and tons have been written about these figures, and they are elaborately documented.
The other group would be the Viking Age Scandinavians who actually existed. About this group far less is known. They left no writings on paper or parchment, and only a few thousand short (and mostly formulaic) inscriptions on stone. Very few contemporary foreigners witnessed them in their own countries and wrote about it. What we have in writing about their lives is mostly second-or-higher-hand accounts of them written by people in foreign countries who had religious biases against them. Or they were written down in the same countries but centuries later (and by people with the same religious biases). We don't really know how this IRL group relates to the former romantic one, although we certainly know they don't fully match the descriptions.
Shield-maidens would belong to the former category. They're well-attested in the Sagas and Eddas, but there are no eyewitness accounts of Scandinavian women fighting in battles. For instance, Saxo Grammaticus tells us all about shield-maidens at the Battle of Bråvalla (Brávellir), which he basically makes out to be an extravagant Viking Olympics blowout where a gazillion fighters from every corner of Scandinavia shows up to chop each other up and even Oden himself gets involved at the end. Yet, apart from the fact that several places named Bråvalla do exist (and they've all been proposed as locations for the battle), there's no evidence whatsoever that the battle ever happened. In any form. And not for lack of looking for it.
So with no hard evidence either for or against the existence of female warriors (much less Shieldmaidens or Valkyries) there's been plenty of debate. The evidence that would be cited in favor of them, is mainly that there are a number of female graves with weapons in them from the Viking and Vendel ages. Both in Norway, Denmark, Sweden and even Finland (where a lady had the fabulous Suontaka sword with her in death, the one seen in the center here) Some specific grave sites are Oseberg, Kaupang, Flisa, Gerdrup.. four graves in Birka alone had female skeletons with weapons. Some of these have been explained with bones getting mixed up, or men being buried together with women where the male bones have disappeared. Stefan Högberg (Swedish historian who wrote the book on the subject Kvinnliga Krigare (2017) 'female warriors') argues that there are turning out to be a bit too many of those 'disappearances' to explain it all, and I'm inclined to agree. There's also been a bias to interpret any grave with uncertain gender as male if weapons were present.
Some of the graves are filled with lots of other grave goods (Oseberg is a very rich one, and was therefore often described as a "queen's grave"). In those cases the swords may be just another indicator of great wealth in the burial of a wealthy, high-up individual. But a few (e.g. Flisa) have little more than the weapon. Just possibly some of these could've belonged to female warriors.
One starting point that isn't behind a paywall is Moen - The Gendered Landscape: A discussion on gender, status and power expressed in the Viking Age mortuary landscape (2010) - PDF link has a bit about it. (her similarly titled book, published Oxford, 2011 has more)
Anyway, so, short answer is we don't really know. It seems unlikely but female Scandinavian warriors may have existed in some form.
