About two weeks ago my sewage ejector pump died and had a massive overflow in the basement. I replaced the pump but I am now noticing that the toilet backs up. I am also noticing that when I take a shower the toilet bubbles.
You have a clog downstream of the pump most likely. It might have even died because of this (overheated?).
You will need a drain auger/snake in order to clear this. If it's close to your access point you might be able to use a small handheld one, but most likely you'll need an electric drum snake:
You can rent these from most home improvement stores.