From what you wrote, it sounds like you were depressed, the depression eased and you were happy, and now you are depressed again, not that you are depressed and happy at the same time. Yes, you can relapse, especially if you haven't gotten any treatment. Your first step is to see a therapist. Many depressions can be resolved through therapy alone. If it isn't enough, after some time, you should check into medication with a psychiatrist.
Yeah, you can. I have been depressed for years but that doesn't mean that i never smile, laugh, or have a good day. How old are you? Im assuming your in your teens cause your talking about school...and being 18 myself I know that teen years are horribly hard..lots of angst caused by hormones changing. The difference between just sadness and depression is that depression is prolonged sadness. Usually lasting 2 weeks or more at a time. Another difference between "the blues" and depression is that depression has other symptoms like weight changes (eating too much or losing your appetite), losing sleep (or not being able to get out of bed), difficulty concentrating, falling grades, losing relationships/friendships, isolating yourself, suicidal thoughts...and other symptoms but those are the main ones. If you feel you are depressed you should talk to a therapist. They can really help. They are non-judgemental people who are there to listen to whatever you have to say and help build you up to be a happier and healthier person. There is medication if you feel your situation is too debilitating too. But medication will only relieve symptoms. The only way you can be depression fully is by getting to the root of it and fixing whatever insecurities or unbearable sadness you may have. Thats where therapy works in.
I wish you well...its a good idea to keep posting on this website. The people are very nice, helpful, and insightful. It can also be rewarding to comment and offer any advice or insight to other posts you can relate to. Keep your head up :)