Great Bridget! This is a really phenomenal question. You’ve hit on a long-time debate in the astrobiology community (astrobiologists are the scientists that study life in the universe, using what we know and discover about life on Earth to try to search for new life in our solar system and beyond!).
The answer is we don’t know! We have strong reasons for believing carbon-based life is the best option. Carbon is a unique element – it supports four bonds and is capable of making long chain molecules. It is this long molecules (such as DNA, and proteins) that make life possible as far as we know. However, alternatives have been proposed. The most viable chemical alternative to carbon is silicon, which also supports four bonds but only forms long chains at extremely low temperatures. It is entirely possible that silicon-based life could exist at way below freezing temperatures we would never even dream of here on our warm Earth! Others have suggested that life need not be based on chemistry at all. Maybe there is plasma life out there (as might live in the Sun) which we might not even identify as living with our current definitions! There are lots of possibilities, and we can’t rule a lot of them out. So I would say, there definitely could be non-carbon life out there but we won’t know for sure until we discover it!