I don't have the twitter library installed, so can't run your code, but the code example below should return the name of the biggest tweeting category. It uses, as PhiLho suggesed, an array to find the biggest tweeter of them all. For just a few categories it's pretty manageable.

kabk?

Code Example (untested)

1. String mostTweets() {
2.   int[] tweetLengths = new int[5];
3.   tweetLengths[0] = numberofHappy;
4.   tweetLengths[1] = numberofConfused;
5.   tweetLengths[2] = numberofBored;
6.   tweetLengths[3] = numberofInterest;
7.   tweetLengths[4] = numberofHungry;
8.   int largest = tweetLengths[0], index = 0;
9.   for (int i=1; i<tweetLengths.length; i++) {
10.     if (tweetLengths[i] > largest) {
11.       largest = tweetLengths[i];
12.       index = i;
13.     }
14.   }
15.  
16.   String mostTweet = "";
17.   if (index == 0) {biggestTweet = "Happy"; }
18.   if (index == 1) {biggestTweet = "Confused"; }
19.   if (index == 2) {biggestTweet = "Bored"; }
20.   if (index == 3) {biggestTweet = "Interest"; }
21.   if (index == 4) {biggestTweet = "Hungry"; }
22.  
23.   return mostTweet;
24. }