"Hishamri Na v'Al Tishti" implies that there is something else she must be careful about!
Radak: She must avoid also Tum'ah, just like a Nazir must avoid Tum'ah and wine. She was warned so the child will be Kadosh from the womb.
Radak, citing Nazir 4b: Shimshon was permitted to become Tamei. We must say that v'Al Tishti explains Hishamri, and Kol Tamei is [other] matters forbidden to a Nazir.
Malbim: Avoid things that by nature are bad for a pregnant woman. Also, do not drink?
What are "Yayin v'Shechar"?
Rashi citing Targum Yonasan: They are new and old wine.
Radak citing R. Eliezer ha'Kapar, in Sifri Nasa 23: It is mixed wine (diluted with water) and pure wine.
What is the meaning of "v'Al Tochli Kol Tamei"?
Rashi: This is [other] matters forbidden to a Nazir. Radak - e.g. anything from the grape vine, from grapes skins to pits, and Mishras Anavim (water in which grapes were soaked) (Bamidbar 6:3,4).
Radak: This is the Perush of Hishamri; beware of Tum'as Maga (touching) and Ohel. Kol Tamei includes eating Tamei things.
Radak citing Targum Yonasan: Do not eat anything Tamei.