Did I get the wrong size snowboard?

No, it's fine. Size is actually determined more by your weight than you're height anyway. A 151 should be a good all mountain size for you. It's true that shorter is easier to control, but you'll advance to an intermediate level in no time so not to worry. You may want to get a shorter board eventually if you plan on riding a lot of park (a 146ish maybe). Have fun!