How do I know I am truly a Christian when I constantly struggle with sin?

One thing I would recommend is to read 1 John. In many ways, 1 John was written exactly for this question of assurance. There are a number of things we are told in 1 John, and one principle is very clear: whoever believes in the Son has eternal life.

It is the object of faith that is the basis of your salvation, not the extent of your faith, not the intensity of your faith, and not the sincerity of your faith. It is faith in Jesus Christ that saves, not the faith itself. First John is going to point to Christ. It is going to point to who Christ is and what He did, which is the basis of our salvation. It is faith in Christ that saves us, and 1 John will help there.

The other thing is your struggle with sin. This gets to your assurance and your sense of fellowship. Even this great confessional text that we talk about, the Westminster Standards, teaches about how your assurance will wax and wane, like the moon. It will get full and it will lessen. It will wax and wane depending on your obedience to Scripture and to Christ. As you have sinned and are out of step with God’s Word, your assurance will wane. When assurance lessens, that is actually a prod for you to say: “This isn’t right. This isn’t who I am in Christ. I need to get back to taking God’s Word seriously.” As you are in step with God’s Word and have an obedient life as a Christian, your assurance will wax.

Ultimately, if our faith is in Christ, that is assurance of our salvation. Whoever believes in the Son has eternal life.