대학교 can mean both college and university. It is shortened to 대학, and often just 대 when it comes after another word (e.g. 고려대 = 고려대학교). 전문대학교 (or 전문대학, 전문대) is the term for two- or three-year college, which usually offers a study of narrow and specific discipline in preparation for specialized jobs. Four year universities are called 일반대학교 (or 일반대학, 일반대) when you need to distinguish them from 전문대학교, but people usually just say 대학교 because there are more 일반대 than 전문대 (roughly 50% vs 40%). 일반대학교 and 전문대학교 are used to refer to the type of school. Schools' names usually just end with 대학교 without 일반 or 전문 (e.g. 연세대학교). For 전문대학교, the name sometimes includes the specialty field, as in '과학기술' in 대전과학기술대학교. Likewise, your Dai Viet College would most likely be translated as 다이비엣 대학교.

Before 2011, 전문대학(usually 2-3 years) could only use the term '대학'. But since then, 전문대학 can use the term '대학교' to call themselves. So nowadays 대학 and 대학교 do not have any differences. However, because it has been divided into 대학(college) and 대학교(university) for more than 50 years, many people still think that those two words are different. Anyway your sentence can be translated into "저는 지금 다비엣 대학교 한국어과에서 공부하고 있습니다."