It looks like you may have damaged the side panel here:
That may make it difficult to tighten the side panel to the bottom shelf and leave the whole thing a little wobbly.
If you're very careful, you should be able to remove the nails from the cardboard backing without causing significant damage to the cardboard. I've done this before a couple of times. Even if you damage it a bit removing one or two nails, you can still reuse it. I usually pry the nail up with a small screwdriver before getting the claws of a hammer underneath to pry the nail out. Be sure to keep the hammer head along the edge of the wood, otherwise, you'll end up pushing a big hole through the cardboard backing and that's not good.
Once you've got the cardboard off the back, release the cam-locks so you can remove this side panel. Take a look at the damaged area here - you may be able to flatten this area by reassembling and hitting the outside (gently at first, harder as necessary) with a rubber mallet to flatten it down. You might be able to smash it back into place by directly hitting the bulge with a mallet, or squeezing it in a clamp.
Alternatively, so long as there isn't an assembly hole in this area, you could get away with chipping the bulged out area away so the two boards can sit tight together.
No, the vertical board won't be quite the same any more, but it's unlikely to cause any significant, long-term structural damage, even if this is a wall hanging cabinet.
Once you've reduced the bulge by pretty much any means necessary, reassemble the cabinet, make sure the cam locks are good and tight, especially in this area. Square the cabinet up and nail the back on again. If you damaged any spots in the cardboard, just avoid putting nails back in those areas. They give you more than enough nails to securely hold the back on and provide structural integrity, so even if you leave a couple out you'll be fine.
If you'd like, you could glue the dowels in by putting a couple of drops of any standard woodworking glue into the dowel holes then inserting the wooden dowels. Some of the flat-pack furniture I've assembled has come with a little tube of glue and instructions to glue the peg into one hole. Some have instructed to glue it into both holes. Most, including those from IKEA, have no glue and no instructions to do so. As far as I can tell, all 3 methods yield reasonably similar structural rigidity. Remember that anything you glue together will be fairly permanently assembled - an important point if you ever expect to take these apart to move them. Do not bother to put any glue around the metal/plastic cam-lock pins, their threads, or the cam-locks themselves. Standard wood glue not stick to these parts very well, and this will simply be wasted time and effort.
Another option has occurred to me.
Since this appears to be a floor standing cabinet, screw a piece of 1x3" lumber (reasonably cheap at the local big-box store) to the uprights at the top back of the cabinet. Two screws inserted through pilot holes into the uprights will help stabilize the cabinet by providing a small amount of additional triangulation. However, more importantly, the solid wood will provide a good material for holding the cabinet to the studs in the wall with a couple of screws. Once it's screwed into the studs, the cabinet won't go anywhere, no matter how wobbly the construction actually is.