Just a few suggestions:
-Remove links/references to games that infringe on copyrights. Including the zelda fan game linked in your cover letter. You can really only sell yourself based on your legal and/or original games.
-Your resumé and cover letter are too long. Be concise. Your employment history doesn't really have anything related to game design on it. This section should be for relevant work experience. If you don't have any feel free to include the most recent and most relevant only, and be concise about what your roles and responsibilities were, they don't need to know every task you performed.
-Your software and skills section is all the way at the bottom of your resumé, below the section about being trained in first aid and being a fire marshal. If I'm an HR person, I'm giving up before getting to your actual skills.
-The Always the Same Blue Sky logo at the end of the resumé is awkward to me. Why is it there?
In total your resumé probably should only be one page long, 2 including the cover letter, and the cover letter doesn't need to take up the whole page. Think of ways to sell yourself succinctly as possible, and then link to your portfolio and personal websites for more in depth descriptions.
In reference to your website, your games section has a lot of games to play with, but no screenshots or videos. It's likely no one hiring you will download your games unless you've already made it deep into the hiring process and they need to differentiate between you and another candidate. Have a quick way for them to get a taste of your work.
Lastly, one month is a short amount of time. QA is usually hired en masse at certain points during the year. So trying to get a job outside of those points is more difficult. As I said before Production/Design roles aren't generally entry level. There aren't really junior designer positions for the most part although things such as level designer are generally more junior. If a company was hiring externally for these positions they would probably advertise them on their websites and/or use a headhunter.
It took me 5 months to get a job after graduation, and even then it was only because I had a friend already working there refer me for a job. Knowing someone is the easiest way in, so keep in contact with old friends who share your interests.