Is my prayer valid, given my doubt during prostration as to whether it was the second or third prostration, my considering it the second, and my performing the prostration of forgetfulness before the salaam?

Whoever doubts during his prostration whether he is in the second or third prostration should perform the prostration of forgetfulness (sujood as-sahw). However, if doubt becomes frequent for him, he should not pay attention to it and should not perform the prostration of forgetfulness. Your prayer mentioned is valid.