After you have experience, degrees are no longer used as an automatic filter candidates.
It'll always be more difficult for you to get a job than someone with the same experience AND a degree, but not impossible.
I strongly suggest doing some online courses (Lynda.com for syntax and training, Coursera for a middle ground between Udemy and Lynda, and Udemy for project work and experience. Udemy offers some kind of degree as well.) and getting some code up on Github to prove that you can actually code.
Many companies are terrified of hiring people with Software Degrees that literally CANNOT code. A Github account is second only to actual experience in proving that you certainly can code.
So get a github account and code till you drop!
You can also create Android apps, which can earn you some money and is practically a requirements if you want to go into mobile app development. I mention Android in particular, as it is based on Java 5 with a sprikling of Java 6 APIs. Lastly, there are conversion courses you can take for people in your situation. It is more common than you'd think for someone to do Arts, Literature, Zoology,
Philosophy, etc (Pretty much any course) and discover that they actually love coding.
You should looking into Masters-level conversion courses and see what you can find with your institution/college.
Good luck!