In this paper, we find all inequivalent classes of self-orthogonal codes over $Z_{p^2}$ of lengths $l{leq}3$ for all primes p, using similar method as in [3]. We find that the classification of self-orthogonal codes over $Z_{p^2}$ includes the classification of all codes over $Z_p$. Consequently, we classify all the codes over $Z_p$ and self-orthogonal codes over $Z_{p^2}$ of lengths $l{leq}3$ according to the automorphism group of each code.