It sounds like you have a good routine going here. When you first got the bizarre buzzing and oozing eyeball, you were definitely experiencing some full blown HH (hypnagogic hallucinations). Your feeling of not being able to breathe was actually a hallucination. Its best to just try and ignore any unpleasant hallucinations. If you would have waited it out and continued to relax, you likely would have started transitioning into the dream state.

It would probably be best for you to perform some reality checks along with your stabilization. I like to use reality checks to help stabilize as well. My preferred RC is the nose pinch RC. Basically, you just close off your nasal passage by pinching your nose. Then attempt to breathe through your nose. In a dream, you can still breathe even though it is closed off.

If you perform some RCs and stabilization techniques and the dream still seems to be a bit fuzzy, you simply may need to just carry on with the dream and engage in some activity. This also may have been why you lost lucidity on the one where you made it into the dream state. When you are new to LDing, idling around without doing much can cause you to lose lucidity.

For stabilization, I recommend performing some RCs, rubbing your hands together and just observing your dream environment. Try to look around and really implant the fact that this is all a dream. Then try to engage in some sort of activity. You seem to have done a fine job of getting into the dream state. Sometimes, it just takes a moment for everything to settle in. If things are still fuzzy, go to a different room, outside, a different area in your dream. See if things clear up in a different area.

Good luck to you and I hope this helped out a bit. If you have any further questions, don't hesitate to ask!