The first thing you need to understand as a Christian is no one is good, only God is. That leaves a simple question though, what is the point of doing good things when we know we aren't good?
Jesus is very clear when he speaks to the rich man that approaches him. There isn't anyone good but God, and if we are honest with ourselves, this is fairly obvious. We have all sinned in some way. In fact just about all of us are guilty of every sin we could be, and that makes us evil. The standard for being good is perfection, and only God has done that. Even one sin is enough to no longer be considered good, so let's not delude ourselves in this area. We like to put people like Abraham or David on pedestals but only God actually deserve to be there.
Now just because we aren't good does not mean that we never do anything good, that can and absolutely does happen. But why does it matter if it isn't going to somehow wash away the bad things we have done? The answer is pretty simple, it matters because it is the right thing to do. Once you put your trust in Christ and repent of your sins, which means to turn away from them, you should legitimately want to do the right thing. It isn't a matter of getting something out of it, we do the things we do because they are right. Once you know something is evil, it makes no sense to continue doing it, it only makes sense to do what you now know to be good. As Christians, there is really no excuse to continue in our sin, regardless of the fact that we will be forgiven for it. God doesn't expect perfection but bare minimum we better be trying to be good even if we are going to fail.
Another reason is simply to please God by doing things that he can take some joy in. God knows all of our thoughts and actions, I don't doubt that he is very happy whenever he sees someone do something genuinely good. That alone is enough reason to do good things, but it's even more than that. Jesus literally died for us, we owe everything to him and doing good things is part of that. It is how we show that we love him through our actions and it is one of the main ways a person can have assurance they are truly saved. If you genuinely care enough about Jesus to do good things for his sake, then even when you fail you can know at least your intentions are in the right place and God is with you. Make no mistake, if you aren't a Christian you aren't going to be doing anything for Jesus's sake, it is almost always going to be all about you.
Another very important reason to do good things is simply to stand out in the world. This is a fallen world covered in sinners and people who are consistently doing things are going to stand out big time. That is exactly what God expects of Christians and make it is important that we aren't just like everybody else. We are God's children and the people around us need to see that, it is a major aspect of giving people the Gospel. If we are consistent with what we believe and live it, when we tell someone the truth it will have more meaning. If we are just living like they are it will barely matter at all because they will be able to see it doesn't actually matter to us.
We always need to set an example and be what God wants us to be. We don't need to be perfect, we are still going to fail sometimes, but we need to try at all times. Doing good things is never going to get you to Heaven, but that was never why we did good in the first place. Let's leave it to every other faith on the planet to lie to people, telling them their good works will wash away the bad. We will keep doing good things for God's sake and for everyone around us that still doesn't know him.
Dedicated to making strong disciples of Christ.