Excellent question, John!

Does God choose me or do I choose God? The short answer is: yes!

The question you’re asking basically asks two things: 
(1) Is God in control of everything? In other words is God ‘sovereign’?
(2) Are we humans responsible for our actions - in particular, for the way we respond to God?

At first glance, it looks as though these two things don’t go together. But the Bible repeatedly holds them side-by-side without implying that affirming one means denying the other.

For example:

In Exodus, we read of Pharaoh, who treated God’s people Israel very badly. Not only was he an oppressive slave master, he also went back on his word when he said he’d let the Israelites go. But who is responsible for his actions? Is Pharaoh responsible? Or is God in control? The answer is: both! Sometimes we read that Pharaoh hardened his heart (8:15; 8:32; 9:12 ), sometimes that the Lord hardened Pharaoh’s heart (4:21; 7:3; 10:1; 10:20; 10:20) and sometimes simply ‘Pharaoh’s heart was hardened’‘(7:13; 8:19; 9:7; 9:35 ). So was God sovereign over what Pharaoh did? Yes. Was Pharaoh responsible for what he was doing - that is was he doing what he wanted to do? Yes - he was responsible for his actions. 

In Genesis 50:20, when Joseph is reunited with his brothers who tried to kill him, Joseph says ‘You intended to harm me, but God intended it for good to accomplish what is now being done, the saving of many lives.’ So again, we see God in control, even when people are trying to do harm. But again, the brothers were not being “robotically” controlled and acting against their will. They really did want to do Joseph harm, and so are still responsible for their actions.

Of course, the biggest place where we see God’s sovereignty and human responsibility together is at the cross. Jesus was crucified because of the evil intent of wicked men. This is a bad thing! But even in their wickedness, these men can’t escape God’s will (Acts 2:23).

Let’s think about this in relation to predestination. How do you know if God has chosen you? Well, you’ll see it in the way you respond! The scenario you suggested - what if I’ve chosen God but God hasn’t chosen me - doesn’t make sense. If you have chosen God, it is because He has already chosen you.

Don’t forget, predestination in the Bible is ALWAYS a positive thing. It is always there to comfort us (e.g. Romans 8:29-30; Ephesians 1:4-14). If you have chosen God, then take heart, because it means God has predestined you to be one of His heirs. Predestination means we can have greater assurance” because if God is for us and has already decided we will be His, then nothing any person can do can take that away. Predestination is not something that should make us more worried about where we stand with God. It should make us realise that since God is responsible for making people Christians, we should be less worried, because the source of our trust is not ourselves, but God Himself.

I hope that has helped. It’s a mind-blowing concept, I know!!