Help with a multi-language medical database
No, you should not split this out into different databases. This will cause more issues and complexity further down the line, for reporting cross country, possibly requiring cross database ownership chaining, etc.

You can achieve your requirements by a process of normalization. Many people say they have normalised a database by looking at the required attributes and splitting them into separate entities by "feel". However, proper normalization is a much more formal, structured approach and is applicable for good database design. There is a very good Wikipedia article at http://en.m.wikipedia.org/wiki/Database_normalization and Itzik Ben-Gans book T-SQL Querying also goes into lots of detail with good examples.

Also recommend that you validate your normalization with a full ERD (Entity Relationship Diagram) Your normalization and ERD are also very useful design documents for your projects documentation library.