Regarding addictive personality: Yes, there is such a thing, but you don't need to have an addictive personality to fall into addiction. But, having those traits does increase your risk. Addictive personality increases your risk for all sorts of addiction, such as alcohol, gambling, sex, even cell phones and internet use.
Even if this does not describe you, being on opiates for more than a few weeks makes you physically dependent. The unfortunate thing is that it is very easy to feel that you still need the opiate long after the source of the pain is mostly resolved. The reason is that the discomfort of withdrawal can be difficult to distinguish from other pain. Your brain is urging you to resume the opiate because of the withdrawal, not because you are still experiencing the original pain. It is an extremely compelling urge. This is the reason you taper and even use other medications to help with the withdrawal symptoms.
Some people say you cannot become addicted as long as you take opiates for pain. But this creates a false sense of security. You do not need to consciously be seeking a high to be addicted. You could be trying to simply avoid feeling terrible when you don't have opiates in your system. I have been on low dose opiates for many years and try to be very vigilant about my use. My rheumy tells me that I under medicate, but my preference is to feel tolerable pain, rather than keep increasing my dose. I KNOW I am physically dependent.
Is it necessary to rid your house of all things with abuse potential? Probably not, but you know yourself better than anyone. Getting guidance from a professional is a good idea, particularly if you tried on your own and failed.
Good luck to you!
Jan