This kind of thing happens all the time actually, in dreams and projections alike. I don't know exactly what causes the issue; from what I have heard, though, I suspect it is primarily an issue of the condition of whatever subtle body you projected in and the degree to which that body can communicate the visual sense. If this is correct, it's similar to clairvoyance; you have an astral body, it certainly can see in its own way, it just needs to communicate those sights. In dreams this may also simply happen when you accidentally blink / close your eyes.
Here's the advice I'd give... like I said I don't understand the mechanism, but I'm fairly sure if you do these things the issue will resolve itself. Even physically blind people should be able to attain astral / mental sight.
1. Until you're more experienced, why should you assume you aren't dreaming? I have no reason to believe that my own projection experiences weren't simply dreams about what I believe astral projection is like. So from this, you may as well try what you'd try in a dream to restore sight, e.g., will yourself to see, ask to be able to see, visualize your surroundings into existence, expect something behind you and then turn around, or spin. There are other techniques but you get the gist of it. For what it's worth, the fact that you tried to open your eyelids and your physical eyelids didn't open gives me the impression that you were indeed projected in some body, but the above is still worth a try.
2. Projections are trickier. Asking why you can't see was a good idea in my opinion, but the technique I've heard more people endorse has been simply demanding to see. Aside from that,. I can't say too much on the subject, but it makes sense to me that working on the middle of back / back side of chest area could help with subtle vision, and it's possible that next time, you will simply not have this issue.
3. Practice visualization in waking life. Your "mind's eye" is not physical, obviously, so practicing visualization should increase the clarity of some dreams and projections, as well as hone your mind so that you aren't startled back into your body as easily.
4. Get more sun if you aren't already, but in moderation of course... this seems silly but it's never a bad bet and the sun is often associated with the eyes in occult circles.
5. The burning sensation you experienced leads me to believe that you've just got some kind of blockage that needs to be cleared. Why not pick up some kind of energetic practice that purifies and exercises your subtle bodies? Don't force anything though, of course, and especially don't try to just force open your eyes during projection.
6. Those entities don't seem malevolent - it sounds like the first was amused and the second helped you out. Still, I know if you've been researching projection that you don't need me to tell you to be careful. However, be careful. There's no harm in trying to keep your projection room a spiritually pure area to reduce the risk of unwanted company. I know it's not a popular opinion that caution is a good idea, and most people in the OBE community seem to be of the belief that it's 100% safe nowadays, but seriously? Better safe than sorry. An experienced teacher would, of course, be best.
Good luck, take care, and congratulations on your success.