To add to Carlo's post, yes the difference is the degree of their meanings. "Hungry" is simply the feeling you have when you have not eaten for a while and need food. "Starving" is extremely hungry; so hungry that you are dying. Some people use the word "starving" in a casual way, such as "I haven't eaten all day and I'm starving!" Of course, they don't actually mean that they are literally starving to death, but it is simply a way to express how they feel; It is an exaggeration. I hope this explanation helps. Let me know if you have any further questions.

"Starving" is the extreme adjective for "hungry" (it just intensifies it). Take a look at these: http://www.ecenglish.com/learnenglish/what-are-extreme-adjectives

"I'm so hungry" is correct in the context. "Starve" means lack of food for a long period of time, and it could lead to death in extreme cases. But "hunger" is your body's natural urge to eat food.