Upvote:2
Yes, under Colombia's visa policy, you may be allowed visa-free entry, as an Indian national who holds a visa (or residence permit) issued by the United States or a Schengen Area country.
However, that does not mean you will be, especially after being notified that you must wait six months before making a new visa application. Appearance at Colombia's border is very likely to be considered a new visa application, regardless of purpose (work, visit, relationship).
Under the circumstances, it may be unwise to test this policy, especially when Colombia's immigrations record would show that you have intentions to work and live there.