Sophomore Chemical Engineering Major: Med School, Grad School, or go straight to employment?

Hi everyone! I am currently a rising sophomore majoring in chemical engineering at the University of Rochester. I’m torn between several different career paths because I cannot figure out what to do. I have always dreamed of pursuing medical school and becoming a psychiatrist because I love learning about psychology. On the other hand, I love being able to apply calculus, chemistry, and physics so a career in chemical engineering seems perfect. My problem with pursuing medical school is that next semester, I would have to overload in order to ensure that all my pre-med requirements are met by the end of junior year. I am signed up for six courses during the fall (General Biology I, Organic Chemistry I, a Chemical Engineering course, Linear Algebra & Differential Equations, an advanced psychology class, and a resume/internship based writing course). I ended freshman year with a 3.60 (is this an alright starting point?) cumulative GPA (fulfilled General Chemistry I and II, Physics I, Calc I and II, English Composition, Statistics, General Psych, chemical engineering courses). While I would love to someday become a psychiatrist, I just don’t know if I can start my career as one when I’m basically 30 years old (4 years undergrad, 4 years med school, 4 years residency). Whereas, if I decide to just pursue chemical engineering, I can choose to either get my masters in grad school or look immediately for employment opportunities before I graduate. Another concern of mine regarding med school is getting the required amount of hospital volunteering, shadowing, research, and MCAT prep while trying to pursue engineering internships. This summer I am currently doing an engineering based internship but I don’t think I will have the time to do this next year while trying to get my medical extracurriculars out of the way. I’m really conflicted because in the case that I do not make it to medical school, I won’t have enough engineering experience if all my attention is focused on medical school for my upcoming years. Any advice on this situation is greatly appreciated and I apologize for this long post!