I can speak from limited experience with downloadable content and the PlayStation Store. I for the 1st time on the 3rd of March bought DLC and it installed itself so my 1st guess here is that for some reason your purchase transaction did not go through and that is why you are being redirected back to the PlayStation Store, it is like they are telling you "If you want to use this downloadable content you have to buy it first"

I bought the Call of Duty: Black Ops "First Strike" map pack and it self installed with no other actions form me and was usable within the game right away with no other action form me. However as this was my 1st "purchase" of DLC I am not sure that this is how it works with all DLC.

I would recommend going in to your PS3 and to the "PlayStation Network" menu option and then in that drop down menu select the "Account Management" option and then in that drop down menu select the "Transaction Management" option and then finally in that drop down menu select the "Transaction History" option and see if your recent purchase of the DLC is actually there.

Another option is to go to the PlayStation 3 menu again and select the "Game" option and in that drop down menu you might find the DLC icon of the software you have purchased. If you see the DLC icon you should select it and follow the instructions given. This has been where the content has gone for me when it has been free DLC Map Packs for Resistance: Fall of Man and you fight find what you are looking for there.

Here is the PlayStation Store FAQ
http://us.playstation.com/psn/playstation-store/purchasing/index.htm

And the PlayStation Support page
http://us.playstation.com/support/

Here is a similar question with additional information
I purchased the DLC costume packs a few days ago, but I have yet to figure out how to access them! Any ideas?

Good luck and have fun!