Is it important to give a full medical history to my plastic surgeon?

Absolutely!
There is a risk with any cosmetic surgical procedure to improve the appearance. It is very important for the plastic surgeon to a document your allergies, medications and medical history as record.
Hypertension, previous blood clots, diabetes, smoking, cardiac and respiratory symptoms do not prevent you from having an elective surgery, but can increase the risks of some complications.
So it is important to be honest to your surgeon prior to  having an elective cosmetic surgery.