What should I do about standing water in my tiled shower?
A tiled shower is generally designed to be watertight during normal use. However, if it is holding water for an extended period of time, it will have a higher chance of leaking or deteriorating more rapidly. Whether it's likely to leak in a way that causes significant additional damage over the next 2 months depends on your house and usage: what's underneath the shower, can you inspect it regularly, how much do you use this shower. It also depends on whether the caulk which seals the corners in your shower has held securely in place even as your structure has shifted. You can mitigate the risk of damage somewhat by cleaning up the standing water using a towel or squeegee after you shower, but it's also possible that your shower is now leaky enough that it should not be used at all. If you want opinions on that, pictures of the shower and the area underneath would be helpful.

You didn't mention the extent of settling that caused your floor to become uneven in the first place. Depending on lots of factors (your home's age, weather conditions, foundation and drain tile, etc.) this could be normal or this could be a sign of a severe structural problem. While repairing the shower may solve your immediate problem, I'd recommend you talk to an experienced builder or structural engineer to better understand this root cause. You don't want to spend money fixing the symptoms only to have them reappear later. Good luck!