May broken safety glass damage lcd screen on camera?

Safety glass on my nikon d3100 is broken, camera works as usual, but need I to change the safety glass immediately or it is OK to change it in couple of months?

What do you mean by "safety glass"?

If you are talking about add-on filters (e.g. Clear, UV) you might as well remove it right now to avoid cutting yourself or leaving splinters in dangerous places.

No consumer cameras I'm aware of have "safety glass" as a feature. If you haven't purchased attachments, you may have broken something that needs repair by Nikon.

The LCD glass must be replaced by a competent repair person.

You must have hit your camera very hard to have broken the actual glass part of the LCD.

My Nikon dSLR's came with plastic LCD covers which protect the glass. My guess is that yours did not

Sounds like the safety glass did its job of protecting the LCD. While it's OK to change it in a couple months, you run the risk of harming the LCD, since you have removed the safety glass. I would continue using the camera, take a little extra care with it to prevent damage to the LCD, and replace the safety glass As soon as possible.