if (inChar == '\n') {
previousTweet == tweet;
No. An equality operator is NOT what you want to use. You can't assign (=) a char array this way, either. You need strcpy().
At some point, you need to set index and tweetIndex back to 0, and put the NULL in position 0 in each array.
You also need to stop posting snippets. How are we supposed to know how previousTweet, tweet, currentLine, currentIndex, and tweetIndex are defined?