I believe that 2122 should be 1112 and 1132 should be 3112. Then, each number describes the digits of the last number.
2=1 2
12=1 1, 1 2
1112=3 1's, 1 2
3112=2 1's, 1 2, 1 3
211213=3 1's, 2 2's, 1 3
312213=2 1's, 2 2's, 2 3's
212223=1 1, 4 2's, 1 3
114213=3 1's, 1 2, 1 3, 1 4
...
Therefore, the next two numbers are 114213 and 31121314. If the error is corrected, then the sequence is 2, 12, 1112, 3112, 211213, 312213, 212223, 114213, 31121314, ...
Solution if an error is corrected