Unlike Spanish, English has a strong, widespread tendency to use abbreviations whenever possible. No such thing happens in Spanish. We could say, practically as a joke to imitate the English abbreviation, things like: "Vive en USA," but this is only allowed in colloquial language. Also, unlike other abbreviations like UK, the initials "USA" form a word that can be pronounced in Spanish as if it were a word in the language.
Surfing the Internet, I just confirmed my suspicion that "Dominicana" can be used as a short form for "República Dominicana."
Notice, however, that the official name is as specified here. In documents from that country I have often seen "R.D.", but this will occur in writing, not in speech.
You can say: "Cuando vivía en la República Dominicana...," or "Cuando vivía en República Dominicana...," or "Cuando vivía en Dominicana..."
In writing only, you can say, "Esto solo se aplica al entrar en R.D."
