Hello! I'm a fellow Psychology undergrad - senior year - and what he said to you is partially true. It is difficult to obtain an entry-level position with a social science degree, especially if you have no further plans to continue grad school. However, it doesn't mean you can't find a job. Nowadays, the field of psychology is shifting toward a more quantitative realm, so it will gain more respect and be seen as a "natural science," even though I firmly believe it already is one.

In most programs, they offer a Bachelor of Science in Psychology, which will emphasize Statistics, Research Methods, and additional math classes. If you plan to find a job with a Psychology degree, it would be wise to gain as much research experience you can. Volunteer in a lab or two, take as many research-based and statistics classes that will actually teach you skills. If you know how to use statistical software programs, like SPSS and R, then you will be VERY employable, especially if research is your niche. It's all about catering your program so you can make the most out of it.

My school only offers a BA in Psychology, but my classes in research method has already given me skills to use statistical programming, which actually got me a job in a lab. My lab supervisor also has lots of connections and I can easily find a lab managerial or research associate position before applying to grad school.

I'm unsure about engineering, but you need to be great at math. Also, getting a low GPA with an engineering degree doesn't look good, so you should decide to go into that route if you know you can handle the workload.