Feeling very dizzy, weak and have a sinking feeling when dizzy, almost on the verge of passing/blacking out. What could it be?

Please get seen soon. It is urgent that you make sure this is not a cardiovascular or neurological problem. Once that possibility has been eliminated, it is likely that you are having panic episodes. If they are frequent enough, you should talk to your primary care doc about it. Although the conversation may flow naturally from her/him if s/he is the person evaluating you for the other problems first.