So you're trying to constrict your vocal chords, right? It sounds like you are focusing too high up in your throat. You're closing your throat around your tonsils, when you should be focusing on restricting the lower part of your voice box (around your adams apple).
It may take some time to find these muscles, I would recommend learning to control the larynx (adams apple) and to speak/sing with the larynx in a high position; then you can keep your larynx up high and restrict the lower part of the voice box for a more feminine sound.
You sound really good when you speak the word "hi"
Also: it sounds like you learned a method of practice from someone that may not be helping you: the technique you used in the beginning to "find" your voice may not be the best method for you. It sounds like smeagol from lord of the rings, which confirms that you are constricting your upper throat behind your tonsils. You don't want to do that. I would recommend finding another method to "find your voice". I always liked starting in falsetto, and then talking REALLY girly and gradually lowering myself out of falsetto.
