Well this is how you can do it. You really don't need string additions( a string +1 is required) . Any way it is better to implement and keep it in your shelf as it may be useful for other problems.
For 808 => it already a palindrome , then next biggest is 818 , increment the middle one.
2133 => it isn't a palindrome => take the n/2 digits make it a palindrome=> 2112 => now it is less than given number => increment the n/2th digit 22 => 2222 is the new palindrome.
2999 => it isn't a palindrome => 29 92 is the number formed =>now add 1 =>30=>3003 is a plaindrome.
Just manipulate the indexes correctly and perform the addition correctly and modify the method a bit you will get the answer hopefully. It would be easier to visualize and convince yourself and coding would be very easy afterwards.