No:
Paragraphs should be used to denote simple actions that are tied together by occurrence at the same point in time. By smushing everything into one paragraph, you have Paul in one instance picking up the hammer, breaking his hand with the hammer, reacting to the initial pain of the hammer (first quote block) could be similar enough actions to bundle together in a paragraph.
However, leaving the work station to find a band-aid, applying it, reacting to the pain (911 call, second dialog, and collapse) are all actions that can not be related to the self-inflicted pain.
As a rule, yes, paragraphs should only have one speaker's dialog, but that is because in a conversation with two people, they do not talk at the same time. Your two quotes from Paul are not happening in the same space of time and are broken up by multiple steps in time and thus should be broken by paragraphs to demonstrate this.
Additionally, there is a lot of missed oppertunity in this blurb to add content. Consider the following actions:
1.) Accidentally inflicting injury.
2.) Reacting to the Injury (OUCH!)
3.) Applying First Aid
4.) Dialing 911
5a.) Second dialog
5b.) Collapsing
These are all elements that could be expanded upon into their own paragraph. Hell, you can eek out a conversation with the dispatcher over the phone that could expand into multiple paragraphs.
Also, the placement of the second dialog is odd. Most people who call 911 realize "This first aid won't do" prior to the call, not after it.
At either rate, option 2 is slightly better but still a problem. Dialog should always open and/or close a paragraph... it should never be sandwiched between narration. Also consider breaking up the dialog by moving your said clauses around (i.e. "Ouch!" He said, "Why did I pick up the hammer?") to help this flow. Ouch is an interjection and usually when you smash your hand, you want to set the immediate ouch apart from the less aware statement. If you go this route, remember that you should not sandwich dialog by narration, which the clause "He said" would be, so this outburst needs to be separated into a new one sentence paragraph (when writing stories, paragraphs do not have to confirm to a set number of sentences).
TL;DR: 2 is better than 1, but not by much. You have too much happening in all of 1-2 paragraphs and need to space them out. Dialog should be as separated from narrative actions as much as possible.