Suggestion: as you may notice from the URL you posted, the space in it causes everything after the space to be ignored. Or, as with your server, it causes the URL to be rejected. That's because it's not a valid URL with that space in it. The parameters need to be URL-encoded. And for that there's a java.net.URLEncoder class with a suitable static method to do that.
Alright now i have a URL to access and when copy and paste it in the browser directly it works fine and I immediately receive an SMS, but when I do save from my swing app, it returns HTTP Response code : 400? Any clues?
Then the browser is sending information that your application is not sending. Since the URLs are the same, that would mean that the browser is sending HTTP headers which your code is not sending. So, you should use some browser debugging tool which allows you to inspect the headers attached to a successful request. I use HttpFox in Firefox but quite likely there are newer and/or better tools, or tools available for the browser you might be using.
By the way... it's quite possible that the server is doing certain tests to make sure you're using a browser to enter your SMS data. It may be possible to circumvent those tests, but before you do that I would recommend reading the site's terms of reference (the terms I suppose you agreed to when you got your user ID). If they prohibit the use of automated connections to the site, then the code you are trying to write would be a violation of those terms.