As a fellow student from a small college, I can understand your concern. I am not sure about your particular school, but in many ways I am concerned that I am losing out on valuable opportunities that can set me apart as a premed. For example, my college does not have a pre-medical society or exceptional opportunities for research due to the small lab facilities. Further, many ADCOMS will not be aware of my college when I apply to the various med schools.
That said, there are some wonderful things about going to a small, private college. Course sizes are MUCH smaller at a small college and you will get to know your professors very well. Personally, my professors have gotten to know me very well and are acutely aware of my interests and abilities. As a result, they are able to supplement my educational experience with special projects and have on occasion tailored their lectures to include topics of my personal interest as appropriate in class. As long as you perform well as a student, you will get excellent LORS from these professors.
I believe that there are benefits and drawbacks to both environments (that is, small versus large colleges). Some of the drawbacks can be overcome by other opportunities, such as the REU program funded by NSF. When push comes to shove, the ADCOMS care about more about whether you are prepared for med school and less about the size of your undergraduate institution.
Stephanie