I'm depressed but I don't think I'm going to tell my significant other.
Why would you want to hide this from your significant other?
I don't want him to be worried about me all the time, I'd rather he doesn't ask me about it
It's commendable that you don't want them to be worried about you but they're your significant other, you should be able to tell them about it. They might be able to help you through it and if they find out the hard way they'll feel terrible about not knowing.
It's not a big deal. I can handle it myself.
You guys are a team though! It is important to tell your partner how you are feeling. Keeping secrets is just going to make problems in your relationship.