Welcome to the violin @stephie, I hope you're really enjoying it! It's been a while since you started this post, so I'll assume that everything is coming along nicely and you're really enjoying yourself, or you've smashed your violin into a thousand small pieces.
As a physically active guy, I'll echo what everyone else said in that you should take it slow, and allow your body to build the required strength, flexibility, and nervous system function to play for longer periods of time.
That being said, everyone likes to measure their practice in "time." It's a simple, objective measure we can use to try to show progress. I read a great article a while ago however, and I think EVERY violinist should read it. It's here: http://www.bulletproofmusician.....-practice/
To summarize the article, "time" is not NEARLY as important as "focus." What's important when practicing is that you're truly focused on what you are trying to do and you have a specific skill you are working to improve when you are practicing. "Mindless practice," as it is called in the article, is about as valuable as not practicing at all.
So, what I'm trying to say, is don't worry about time. Worry about building up your body to play the violin, take time to focus during practice and avoid distractions and mind wandering, and just enjoy yourself. The rest will come.
Disclaimer: I'm a complete novice.
There is no failure, only results.
My arms got sore too when I first started, so I cut practice time down some, after a while my arms started to be able to hold out much longer, to where I can actually use them now for 2-3 hours, with some stretching and relaxing in between. I'm neither physically active nor strong (my 8 year old is stronger than me, lol)
It's easy to play any musical instrument: all you have to do is touch the right key at the right time and the instrument will play itself. Johann S.Bach
I agree with the fact that 10, 15 or 30 minutes of focused practice can be more productive than 1 or 2 hour session. Even if you don't have time to pick up the bow and play (for example at night), it's better to use 10 minutes to do some bow exercises or "smack" yours fingers into the fingerboard than nothing at all. Things like these are just important as actual playing and it's still practicing.
Other concept is mental practice. By closing your eyes and imagining your movements and how will it sound or just by reading the music sheet away from the instrument can actually help you the next time you play. In the end, just like wookieman said, time isn't as important as focus.