Once I asked my chiropractor how come I could do something strenuous or long lasting like weeding, planting or moving furniture, be fine when I stopped and then, after a rest watching tv or having had a nap, my back would then be agonising. He explained it thus: when you've done something that makes demands on muscles, you need to do gentle stretches or some cool down exercise to let those muscles recover from the activity.
So you said that you are fine until after you've driven home so I would suggest that is your problem, even though you don't say how long the journey is. So I suggest you have a word with the trainer at your gym and get him to plan some cool down stuff and stretches in order to obviate this problem. Let me know how you get on with it.