I feel like after 10 seconds of thinking....

Your problem is that you overthink a situation and then you confuse yourself. Try taking notes on moves you're thinking of. Then practice just thinking of one thing at a time. I used to have this very same problem. Hope this helps and good luck!

After 10 seconds I haven't even started figuring out the implications of my opponent's last move let alone have any idea what I'd want to do in response. 

The key is just being systematic. Pick a move selection process (every author these days has one to choose from) and use it until it is habitual. 

Basically, they all come down to some version of: 

1) figure out why your opponent made his last move. What are all the things that his move changed on the board?

2) figure out all the different ways you could response to his move that forward some tactical or strategic idea you have for the position.

3) test each of the ideas from step 2 by walking through his possible responses and keeping a "top" move in your mind that you only reject if you find something better.

4) Decide on your move.

5) blunder check your choice.