Don't worry, your trem will be fine. Here's the problem. When you put the springs back on, you didn't set the trem in the groove of the 6 screws that hold the trem on the guitar. There is a groove around each of the 6 set screws and there is a knife edge in the flat part of the trem that needs to be riding in the groove. Here is a picture of my trem. Look closely at the screws in focus at the closest part of the trem and you will see that the plate is lower on the screws than the ones in your photo. Just loosen the strings again and jiggle the trem until it settles into the grooves and then tighten the strings again. When it is right you should have a little of the screws sticking up out of the trem flat part like in my photo.
You should also have 1/16th of an inch clearance above the guitar body for the trem to move which it looks like you do. The last thing is you should tighten one of your claw screws (or loosen the other one), so that all 4 springs have the same tension. Your claw looks a little uneven.
Let us know when you have it working again.