Engineering or Statistics - Question about Calculus Sequence

I am passionate about pursuing a major in engineering/math/statistics. I am currently taking Calculus II at a local community college in Illinois due to time and money constraints. Great instructor and great tests but due to time constraints he is skipping almost all of the proofs for theorems and not giving any questions involving proofs in tests. I am wondering if that is how most of the high school students are taught and whether I will be ready for the rigorous courses in college. Any suggestions?

A physics professor advised us to take all your major courses at WashU and electives at local colleges in the summer.