1) Even though a person is allowed to make personal requests during the Amidah, he should not do so during the first and last three blessings, as with them he arranges the praises of Hashem, and it is unfitting to use them to make personal requests. (Shulchan Aruch and Mishne Berurah 112)
2) However, it is permitted to use them for public requests as this is also a praise of Hashem that everyone needs Him, and it is for this reason that we say “Ya’aleh veyavo” in the blessing of Retzeih. (ibid)