I inherited a painting from a relative. It has some cracks so I assume it's oil, not acrylic or watercolor. I also do not know the age, but it is not new.

When I bought a frame to fit it (since it didn't have one), the frame came with a pane of glass.

Will I damage the painting if I place it in the frame behind the glass? (Because I already did. *It's been there for a couple of years*.) If so, what can I do to mitigate the damage? 

There is no visible damage to the painting, I'm just concerned.