Getting a decent resume and sending it out to other companies didn't cost you anything but time and effort. Things may not come up right away, but you have a job that pays the bills so no huge rush. In the mean time let it be known at work that you'd like to progress yourself and work your way up, again it wont happen over night but its a potential opportunity.
Going into work grumpy and with a take no bs attitude probably wont help things at all, you need to stand out from the crowds, be the person who get things done promptly and with a smile. Your company arnt going to pay you more or help you to progress if its obvious you don't want to be there.
My last job was only for 2years as it was a crap place to be, even though I didn't like working for them I still put in 110% whilst keeping my eyes open for something better. That's now paid off as something much better came along.
Getting a ne job or improving the one you e got isn't all about experience or time, its more about your attitude. Id often chat to my last boss about potential new recruits, some of them had no experience in this industry at all but they got taken on as they seemed hard workers.