Double Vision and Glasses ???

Actually, although it may be astigmatic deviation that needs correction, I don't really think so. I don't think refractive error is the reason he gave you glasses to correct "double vision". If it is true double vision, he has probably induced prism into one or both of the lenses in order to bring your sight back into focus. What's happening is that one or both of your eyes are not focusing at the same spot in the distance, hence, double vision. Prism will (simply put) move the central vision of one or both eyes right, left, up, or down or a combination of those (called compound prism) in order for both eyes to focus at the same spot. (Simple explanation)

There is such a thing called "press on prism". We do it for higher order deviations where the prism cannot be ground into the lens. So, this "press on" material is applied to the lens. It was weird. I put the glasses on and looked straight ahead and what I was actually seeing was about 45 degrees to the right of me however, the person who needed these glasses would be seeing straight ahead. But, you don't have such severe issues like that and the issue you have is not likely to progress further than it is right now.

So, the answer to your question, (if you have true double vision and not just blurriness) is, Yes, glasses will help.

Whether you will be able to "quit" glasses, the answer is ... "Maybe, but I woudn't count on it". An old addage in the industry is "never take prism away".

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Some types of astigmatism/double vision can be remedied by eyeglasses.

Astigmatism is caused by a slight mis-shaping of your eyeball [usually permanent], so you will probably need to use corrective lenses from here on.