It sort of depends on how much you eat and how often. I agree about being tested for low blood sugar, but you also should take a look at whether you're not eating enough at meals and then going too long between meals.
Also, if you haven't eaten in a couple of hours and then do a workout, you could easily find yourself feeling shaky.
Making sure you eat protein with every meal and snack can help you get less hungy in between. It doesn't have to be a steak

it could be some yogurt, lowfat cottage cheese or string cheese, some tuna, a boiled egg, etc.
Jay