It might be worth while to ask your employer if you could get some constructive feedback on what has stalled your progress at your current job. You could phrase it along the lines of "What sort of improvement could I make that might lead to me advancing?" Then listen quietly and resist any temptation to get defensive. Just thank the supervisor for the feedback.

You need to figure out if your lack of advancement is due to staying at this particular job, or to some problem that you will take with you wherever you go. It could be some of both. I notice you say in your status that you are "trying to figure out" what you want. People who have a firm, solid idea of what they do want tend to have a lot of focus and that can really organize their whole approach to life. I've never been that way, myself. My own life is a testament to the maxim: "If you haven't got a target, then don't be surprised if you don't hit it."

You don't sound fascinated by this job. If you're a smart person, that could be part of the problem. Jobs we are really passionate about can be hard to come by. You are right to be cautious about letting your current employer know you are shopping around. I agree with much of what's been said above.