To answer your main question -- no, you definitely don't need any pub to get into a decent social psych program. Just show that you can think critically and independently about psychological research and have a mature idea about what you want to study in grad school -- this is enough I think. Your research experience definitely helps show your strength in conducting research, so it is pretty good! I'd say that your overall GPA is a bit low but otherwise your profile is pretty solid. Maybe you can retake the GRE to improve your quant a little bit, if you have time -- but it is not necessary. Good luck