Ma'am - unlikely on a relatively short-haul flight to Rome. Deep vein thrombosis
does occur from time to time with some people who take long-haul flights and for those with medical conditions susceptible to this. Your friend is much more likely to have suffered a heart attack
from existing medical conditions than from the flight itself. Of course, smoking
does not help in any activity in life.
You may have heard of those special stockings which you can buy to reduce the possible effects. If you are really afraid, this might be worth investigating, as they are cheap to buy. Hospitals use these for patients who are going to be bed-ridden for a while. The stockings are comfortable, look nice and are effective.
As you say that you have two weeks before your honeymoon journey, I should re-book on a cruise ship, many of which are now 'aimed' at younger people. Slower, more comfortable - and much more romantic! If you 'shop around' you can get some good deals. Depends upon your budget, of course.
Any form of travel involves risks - as does staying at home! As long as you sensibly weigh up your situation and balance them against your fears, one person's misfortune does not mean that it will apply to you. As you are young, despite your lifestyle, I would be amazed if you had problems - apart from at the airport, checking in, delays, cancellations, etc.!
Have a great time and when you come back, continue with the lifestyle improvements you mentioned!