I just found out that I'm pregnant, but I don't think I should tell my partner.
I'm not sure you've thought this through. Why don't you want your partner to know you're pregnant?
I don't want to give him a lot of stress.
Yeah, he might be upset but that's an awfully big thing to keep secret whether you decide to keep the baby or not. You'd basically be lying to him. You should try to talk this over with him, especially if he's the father of the child.
He is going through a lot of stuff at the moment, he is working hard to help us and I will be the one taking care of the baby.
It's normal for parents to share the burden of raising kids, so there's no need to feel guilty.  You need to tell him, so he's prepared when the baby arrives. He'll probably freak out if you spring it on him at the last minute.