The Biomedical Vancouver style is not one normally provided by EndNote. Instead, it is a style agreed upon by the Biomedical Sciences academics and created by library staff. That is why it is available on University PCs, but not on your personal version of EndNote.
For your own copy of EndNote you need to download the style:
Note: if you are unable to save the style to the folder in C: (e.g. if you need Admin rights to do so), you can create an EndNote Styles Folder in another suitable location and point EndNote to this new folder instead. To do this: In your EndNote library Edit > Preferences > then in the grey box select Folder locations and your Style Folder location.
If you are using EndNote on a campus PC, please use the link to our 'How do I change my referencing style in EndNote?' FAQ.