Since we were in Persia because of the Babylon captivity, was the messiah concept obtained from Zoroastrianism.
No, Judaism had a belief in moshiach before zoroastrianism was invented. While zoroastrianism is a very old religion it isn't older than Judaism. As for the Jewish belief in moshiach see Rambam:
Anyone who does not believe in [Mashiach], or whoever does not look forward to his coming, denies not only [the teachings of] the other prophets but [also those] of the Torah and of Moses our Teacher. For the Torah attested to him, as it is said: “G‑d, your G‑d, will return your captivity and have mercy on you. He will return and gather you [from all the nations whither G‑d, your G‑d, has scattered you]. If your banished shall be at the utmost end of the heavens [G‑d, your G‑d, will gather you from there]… and G‑d, your G‑d, will bring you [to the land that your fathers possessed, and you will possess it]…
The time line discussed in Wikipedia seems to say that Zoroastrianism was invented some time around the destruction of the temple (or shortly thereafter). As a result, one can say that many of the concepts of Zoroastrianism were actually adapted from Judaism rather than the other way around. However, there is no real proof as to what actually happened.