Do I have strabismus, amblyopia or something else and can anything be done for what I have?

I have always had some issues with my eyes starting since I was very young. I have had a surgery to correct what was diagnosed as lazy eye when I was 6 months old (used a patch then too) and again when I was 3 years (do not believe I used a patch this time). The surgeries never seemed to have much effect at all if any really and I continued using mostly only my right eye. As I did this, the vision in my left eye worsened as my eyes did not work together. I remember around age 6 not being able to even look at my nose with both eyes at the same time no matter how hard I tried, but only with using one eye at a time. When I was about 12 or so I began using contact lenses instead of glasses because of intolerable headaches caused by using the glasses. My left, weak eye could be corrected properly with both the glasses and lenses but when the lense I used for my left eye was stronger and gave better vision than my right eye, I began to use only this eye instead! After a few years my eyes began to not tolerate the lenses and would burn continuously when I used them, even when trying different brands and thus I have went without for a few years. So recently, (I am now 19 years) the matter came to my attention again when watching a 3D movie. I noticed that I somehow can now use both eyes at the same time if I consciously try to (I can look at both sides of my nose at the same time now too!) but because the vision in my left eye is so poor, I get a horrible headache when my eyes try to focus and merge the two images from each eye when one image, from the left eye, is so poor quality. I can however manage this when what I am looking at is close to my face and preferably does not contain too many words to read. At a mall a few weeks ago I tried the new 3DS and was able to see the images as intended so I can at least to some extent perceive depth for I notice a lack of this depth when the 3D option is turned off which I tested. So I am wondering what could be going on. Are these conditions fluid and can be corrected or at least improved through vision therapy or something of the sort? I would imagine so since my eye abilities have changed drastically throughout my life. Also, would it be a possibility for my eyes to be corrected through surgery to give the possibility of training them to work together normally? It feels as if my eyes want to work together as I can make them do so even for long distances and even though the poor eyesight of my left eye gives me a headache when doing this, the eyes seem reluctant to go back to using only the right eye again. So I am just considering my options... Thank you to anyone willing to help.