I wouldn't say possibly, I would say probably. I believe your memories are connected to a past life, yes.
I think most children do come back with past-life memories, mixed in with childhood fantasies. Christian parents are understandably unsettled by this and discourage their children from believing they were ever "big" before, or "drove a car" or "wore a uniform", etc. But sometimes the memories are much too strong and vibrant to forget — and I think more often than not, memories involving sudden or emotional or brutal deaths in the former life stay with us. If we don't recognize them for what they are, they come to us in recurring dreams and nightmares. http://www.dailymail.co.uk/femail/article-1209795/Reincarnated-Our-son-World-War-II-pilot-come-life.html is an article on a recent case, but there are many other recorded cases of past-life recollections like yours.
WW2 was an earthshaking period in history, especially for Europeans, so it's not surprising that anyone who died during the madness of that era would come back as a child haunted by memories.
You really should get a few books that could help you come to terms with your past life. A quick check at Amazon and you'll find several books that can help you remember more, and more accurately or clearly. The main techniques they teach are meditation, self-hypnosis and dream interaction. Because you have such strong dreams, I would recommend a good book on interactive (or lucid) dreaming, such as "Creative Dreaming" by Patricia Garfield. A good book on how to interact with your dreams can teach you how to communicate with your dreaming mind and use your dreams to answer questions and solve mysteries.
If you don't have a past-life journal, definitely you should start one. Put everything down in writing, all your feelings, impressions, memories and dreams (even the dreams that don't seem to connect to a past life event might hold clues). When you start putting together all the pieces, you might even get a clear enough picture to verify your previous existence through public records. That happens more often than most people think.
If you haven't looked in at this site, you definitely should: http://www.childpastlives.org It's for everyone who has past-life memories. There's a moderated forum there too, if you'd like to become a member and join the community.
PS Follow what you know to be true and ignore the religious criticism against reincarnation. Reincarnation has always been a part of ancient Judaism - see http://www.youtube.com/watch?v=mM8dn68vgD8 for example - and it was, naturally, a cornerstone of original Christianity too, as taught by Jesus. In the 4th-6th centuries formal Christianity was modified by Roman emperors such as Constantine into a more pagan (and less Jewish) religion. There's plenty of historical evidence (unbiased) if you want to do more research there. By the way, I was good friends with a very devout biblical scholar and Methodist minister, who was also a Reincarnationist. Christian Reincarnationists do exist, more than will admit it, because of the public's inability to understand how reincarnation works within the Jewish/Christian religions.
And don't forget Carl Sagan. Carl Sagan - brilliant scientific mind behind the "Cosmos" miniseries and books, part of the science team for the Voyagers spacecraft - and known for his tireless dedication to debunking claims of the paranormal. As a serious scientist, Sagan detested the "baloney" in the so-called supernatural world, and even founded a group specifically to examine and debunk paranormal claims. But after looking into the studies conducted by serious researchers, such as Dr. Ian Stevenson, in the field of reincarnation, Sagan was so impressed that he concluded [emphasis mine] that reincarnation is possible:
"At the time of writing there are three claims in the ESP field which, in my opinion, deserve serious study: ... (3) that young children sometimes report the DETAILS OF A PREVIOUS LIFE, which upon checking turn out to be ACCURATE and which they COULD NOT HAVE KNOWN ABOUT IN ANY WAY OTHER THAN REINCARNATION. I pick these claims ... as examples of contentions that MIGHT BE TRUE." - "Demon-Haunted World: Science as a Candle in the Dark" by Carl Sagan (pg 300)