In a word YES. Absolutely. To take an example that is not related to backs – the relationship between pain from arthritis in knees is almost completely unrelated to the severity of bony changes to the knee itself.
But if you look at anxiety levels and compare them to pain there is a very strong relationship.
So yes your anxiety is probably leading to more pain. However, your anxiety is probably leading to avoidance of certain activities, which is in turn making both your mental and physical states worsen.
My advice, bearing in mind that i’ve not examined you and have had a few pints is that you need to keep yourself moving and exercising. That will help both your mental and physical wellbeing.
There is nothing to stop you from becoming pain free, but you will need to work at it.
If you want any more specific advice my email is in my profile.