Yes, it is, but it is harder without an internship or some experience. Here's the deal -- employers hire talent. They hire skills, ability, and attitude. There are two ways to demonstrate you have those: 1) a BA/BS degree from a reputable university, and 2) real world experience and references.
The good news is that you are showing a good work ethic, focus, and time management by working and going to school -- even if your work isn't directly related to your major. Since you having even selected your major, you really need to think about your financial situation, if you are willing to get loans, and if you are willing to give up your daycare job to take an internship or part-time job closer to your field of interest once you have some skills.