Well, there are various possible causes for this.
1.You may be suffering from strabismus. You can correct this problem by wearing glasses which has prisms inside. You can also have eye exercises which the doctor gives you.
2. You are likely to have nystagmus, a kind of involuntary eye movement. This may be caused by inner ear diseases, medication, stroke, tumor and many other diseases.
No matter what it is, you need to go to see a doctor as soon as possible.
You may get the eye twitching problems from your symptom of moving side to side. Your eye twitching may be caused by the coming invisible bacterium. You need to use the eye drops with anti-inflammation to make your eyes get moisture and comfortable. You could also use the warm compress to make your eyes feel comfortable. In addition, you could also eat more food with vitamin C to moisture the eyes.
I am afraid may be you have got a squint. It is related to refractive error. I recommend you to go to see your doctor as soon as possible and do what your doctor tell you. For that heavy squint needs to be cured by operation. But you may just got a moderate squint as you described. So don't worry. May be you can cure it by relax your eyes. There are three ways maybe you can have a try. First, looking far into the distance. Second, with your right eye shield by one hand , you can use the left one to look into your left ear direction. One second later, you can use your right eye to look into your left eye direction. The last one but not the least, you can do eye exercises every day.