What sort of music do you like? A lot of composers can be turned off, or get frustrated because they are writing things that they themselves don't like. So are there any composers you like? I grew to like Holst and Vaughan Williams because of playing them in band. So my first compositions were usually based off folk songs.
Also, write what you know. You play violin, so you probably don't want to start writing for brass just yet, or harp, or something that you don't know too much about. You might want to try a string quartet. (Cello, Viola, and two violins). Composers have been writing for quartet for hundreds of years in all sorts of styles. Personally I stay away from quartets because I'm not too good at writing for such a small group of strings (mostly because I've never played a string instrument). But you would be perfect for that!
This is the wiki article for string quartets if you are interested in writing for that: http://en.wikipedia.org/wiki/String_quartet Check out the "notable string quartets" section about halfway down if you want some ideas.
You also might try writing for unaccompanied solo violin.
If you can only write a couple measures - take that couple measures and repeat it in a sequence a couple times and add a transition. All of a sudden you have an A section. Now just write a contrasting section (perhaps in the minor if you started in major, or visa versa) and you have a B. Now just repeat the A section, perhaps with a couple small changes, and a nice ending, and you have a great piece of music!
1-2 minutes may not seem like a lot when you compare it to a symphony, but most every composer writes dozens of short pieces to every long. Plus if you write a couple more 1-2 minute pieces that are similar, then you can throw them in a suite, and presto! you're a legit composer!
Hope that helps!