Is it conditional like the same as saying 「なら」?
ったら is not really a conditional in the way
なら is, although it does look like etymologically it came from the conditional
たら. In terms of meaning, it's used to gently express a combination of mild surprise and embarrassment or criticism. See here (in Japanese).
There's a fairly good explanation here on HiNative, but basically
私ったら is expressing mild surprise/shame at one's own actions. You might think of it as the
Oh my in
Oh my, what a klutz I am. Like English's
Oh my, it's not used much in actual conversation.
That said, it's hard to say anything with 100% certainty without context.