How do you stop your voice from straining when singing?

You've already discerned that you're doing something wrong - and you are correct. Continuing to sing when it feels like you are "straining your voice" will ruin it. You really need to work with a good voice teacher. They can give you (specifically "you" - it differs from one person to another) many techniques to eliminate this insidious habit. Find a voice teacher - you'll never regret it.