what a lovely ring. I can see why it's special to you. If you enjoy wearing it everyday - then - wear it and enjoy it! I think it would be advisable though, to get the ring appraised or at least the stone identified, if you suspect the stone is gem material.
One quick way that would indicate the stone is a natural gemstone and more expensive than glass, is by examine the facet lines. The larger the stone the easier this will be to detect. Are they sharp and precise facet lines? Natural gemstones have to be cut to their best advantage, whereas synthetics and glass facets are more rounded and not so precise. A jewelers loupe is essential here.
When someone asks you to name a green gemstone, people mostly think of emerald, but there are many other green stones.
Green Birthstones are the following: AUGUST - PREIDOT MAY - EMERALD OCTOBER - OPAL & TOURMALINE
of those green gems, polished gemstones, range from transparent to opaque depending on how much you can see through them.
So if you mange to determine the green stone from the above list, you then have to determine whether the green stone is synthetic and if it has been treated.
practical hands-on experience is essential in identifying a gemstone and for those interested, I recommend taking every opportunity to look and handle gems. There are gem study courses available and practical workshops and teaching centers that provide hands-on practice for students. Gem shows are another great way of getting acquainted with gemstones.