It is permissible on Yom Tob to carry from one domain to another, and to carry within the public domain, even without an Erub, as long as this is necessary for the Yom Tob itself. Even if one carries not for an immediate need, but for later in the Yom Tob, carrying is permissible. Thus, one may carry a Siddur or Mahzor to the synagogue even if he does not need it immediately. For example, if a person will be praying in one synagogue for Shaharit and in a different synagogue for Minha, he may drop off a Siddur in one synagogue in the morning along his way to the other synagogue for Shaharit.
It is also permissible to bring one’s Siddur or Mahzor home from the synagogue after the prayer services. Since Halacha allows him to bring it there for the prayer service, he is allowed to bring it home afterward, in order to avoid the risk of losing it. Preferably, one who carries home his Siddur or Mahzor should use it at some point during the Yom Tob, such as for Kiddush or the Azharot, though strictly speaking he may bring it home even if he does not use it again during Yom Tob.
One who requires medication during Yom Tob may take the entire bottle of pills with him when he goes out, and he is not required to take only the pill or pills that he will need. This is similar ("Le’habdil") to the ruling of those authorities who allowed smoking cigarettes on Yom Tob, who ruled that one may take the entire pack with him, even if he will use only one or a few cigarettes. We my apply this ruling to the case of medications, and thus one who goes out on Yom Tob and will need medication may take the entire bottle, and does not have to first separate the pills that he will need. This is the ruling of Hacham Ovadia Yosef, in Yalkut Yosef (p. 232).
Summary: It is permissible on Yom Tob to carry from one domain to another, and to carry within the public domain, even without an Erub, as long as this is necessary for the Yom Tob itself, such as carrying a Siddur to the synagogue. One may also carry the Siddur home from the synagogue, even if he will not use it again that day, though he should preferablys use the Siddur again at home, such as for Kiddush. One who requires medication on Yom Tob may take the entire bottle of pills with him, and does not have to first separate the pill or pills he will need.
