Every time toilet gets flushed or sink faucet is turned on the person in the shower gets doused with cold water. Is there a cartridge that can be added to prevent this?
Do you mean the person in the shower gets doused with *hotter* water instead? That's what should happen if the toilet is flushed or sink faucet is turned on.
If so, you could probably alleviate the increase in shower temperature somewhat "for toilet flushes", until you install a pressure balanced valve. Try partially closing the valve that feeds water to the toilet to allow only about half the water flow to refill the toilet tank. This should reduce the amount of cold water "robbed" from the shower. The negatives of course will be that it will take twice as long to refill the toilet tank along with more water refill noise.