If you did not have a lot of overnight call as a med student, this may be new to you. You will adjust. That doesn't mean you won't be really sleepy sometimes. Just not quite as sleepy.
Drinking lots of water and eating crunchy food helps me. Sometimes an apple or a bag of chips can really keep you alert. Also works when driving, except if you drink too much, you'll have to stop.
I really don't think taking an OTC is the best idea. Even caffeine has a nasty side effect profile. If you think you have excessive daytime sleepiness, you could see a sleep specialist and get something prescribed to you. They'd probably want to do an multiple sleep latency test on you, and maybe a sleep study if you think it's a medical condition and not just internship kicking your you know what.