Ruby, here is the difference: "I'm always" describes a person. ("I am always") "I always" describes what a person does.

"I am always" usually means that I always do something and I am doing it again right now: I'm always hungry, I'm always late, I'm always studying. "I always" should mean that you are describing yourself, or action that you always do: "I always eat when I am hungry," I always wake-up late, so I am always late to school," I am smart because I always study." I hope that I explained that well. I always try to do my best.

"I'm always" is a declarative verb form, and this is the normal way we use verbs in general conversation. "I always" is an imperative verb form, and means are giving an instruction, even if it is to ourselves :)

'Always' is an adverb. It has nothing to do with whether you should use 'am' or not.