Tweets showing up that I didn't write?

I just made a twitter about a month ago, but I haven't really done anything with it. I'm following one person, and haven't made any tweets. Well on two separate occasions I checked it and it said I had a tweet. They were both like these odd humor ones with some link with it. The second occurance was today, so I deleted it and changed my password. I looked at the apps and the only ones I have are the ones to connect it to the iPhone. Any suggestions?

Maybe it's a family member trying to mess with you, or it could possibly have been somebody that got into your account. It sounds odd that somebody would want your Twitter account. But you made the right choice in changing your password. I would suggest waiting to see if this happens again, if it does, then i'd try changing your pass again and take any precaution available, and keep your iPhone with you at all times. It might be a family member/friend trying to troll you.

Someone must have discovered your password. Or, you left yourself logged onto a device in which somebody else has access to. Remember to log off when you are done, unless on your phone, which, as long as you keep it with you, you should be fine to keep that logged in. But if they are getting access through your phone, put a passcode lock on it to keep it safer and more secure. If on a computer, just remember not to stay logged in.
If it does happen again, change your password again. But if it happens again after that, then it is more likely that it is somebody in your household or one of your friends or somebody who can get access to your phone or whatever device you use.