Traveling with many prescriptions to TCI this June.

Will I have issues if I am traveling to Providenciales with my anti anxiety meds and 2 strengths of valium plus some other meds that are needed to continue my taper off valium? I have all containers with labels and can get a doctor notes for my meds and my condition but don't want to get arrested or fined with controlled substances that are my personal prescriptions. I am not bringing narcotics or opiods or barbituates or amphetamines or marijuana which is stated on one of the sites. I want to make sure I will be ok? There is no one to reach to get approval so all I have is a doctors letter and the drug store receipt for the item which is basically the prescription. IN THE PAST I have never had my bag checked but I want to be prepared since they seem to be searching now with all the bullets.