Good luck!I live car free in a very car-centric city personally, no regrets.
The bike trailer really works well for large grocery shop runs. Sure, it is heavy, but I just see it as extra bike training. The low-cost trailer I use, from a brand named Aosom, has been working really well for even big bags of cat food, large crates of beverages, etc. :
https://www.aosom.com/item/aosom-eli...664-0005R.html (they sell it on Amazon as well).
For smaller grocery runs, or smaller things to carry, I just use the paniers. Also a bungie cord over the back rack is very useful for larger items that don't fit in the panniers. (long items or cardboard boxes).
The biggest hurdle people think of is not having a safe route to your daily destinations. But I often find there is almost always some parallel route you can take through a residential neighborhood that does not involve using major arterial roads. Over time, you find quieter and safer routes to all your daily destinations.
Also, between services to get groceries delivered (instacart and the like), services like Uber and Lyft, and ride-share options you can sign up for like Zipcar, there really is no eventuality that is not covered. You can always find a way out of trouble if you really NEED a car for some scenario. It has never been easier to not own a car.
Good luck! You are doing the right thing!