Now I'm back in school and it's getting busy again. But in the classroom, I always get distracted thinking that I am doing something wrong when I'm doing the work. I obviously know that homework is not a sin, but it feels like when I get busy with work I just lose sight of God and forget about Him. Is this a problem? Also related to this I really want to live for God and to work for His kingdom but I don't know what to do. Going to preach to strangers as well as friends seems really scary. I hope you can help me with some insights into this.
I hope you realize that it is God who teaches, "For even when we were with you, we commanded you this: If anyone will not work, neither shall he eat" (II Thessalonians 3:10). And in that working, we are directed, "Bondservants, obey in all things your masters according to the flesh, not with eyeservice, as men-pleasers, but in sincerity of heart, fearing God. And whatever you do, do it heartily, as to the Lord and not to men, knowing that from the Lord you will receive the reward of the inheritance; for you serve the Lord Christ" (Colossians 2:22-24).
Though you are not yet working for another man, still you are preparing to work in your schooling. Doing a good job at what you do is a reflection upon the God we serve. I remember in High School struggling with grammar. I had already decided that my chief goal in life was to preach. But I remember getting a poor grade on one paper and foolishly telling my teacher that it didn't matter because I wasn't going to be a writer, I was going to preach. How little did I know how much time I would spend preaching through the medium of writing. I've "eaten" my words many times.
It doesn't matter whether you are learning carpentry. Make beautiful cabinets because it is a service to others. If you are mechanic, do a accurate job because it keeps another person safe. Whatever you do, do it with the attitude that you are serving God while serving others.
It really comes down to a matter of priorities. Nothing in this world should become so important that you put it before God. "But seek first the kingdom of God and His righteousness, and all these things shall be added to you" (Matthew 6:33). But God isn't asking anyone to ignore everything else. "But if anyone does not provide for his own, and especially for those of his household, he has denied the faith and is worse than an unbeliever" (I Timothy 5:8). It has always been a matter of which comes first in our life, not which is exclusive in our lives.
I'm glad you are interested in preaching. What you should do is seek out opportunities to speak both publicly and in private studies. Those early studies won't always go well. Points are going to be made that you will have no idea how to answer. That's fine. It is part of the learning process. You go home and you start researching the answer. You ask preachers for help if you get stuck. I know there are some questions that have taken me literally years to come up with an answer that I was satisfied with. But now that I've learned the answer, I can handle similar questions quickly.
Also, remember your imagination is much more "productive" than reality. While talking to others seems scary when you haven't done it much, you will find that the reality is not nearly as difficult as you imagined it to be.
As you progress, find preachers you admire and study under them. Learn how they handle situations. Ask to go with them on studies so you can see how they handle them. Present lessons when they are there so they can give you pointers. Then when you feel it is time to preach you will have a wealth of experience to draw upon.