Good questions and concerns... And sorry you are hurting.
Generally some pain is associated with any extraction. However, a more intense pain which generally occurs 48-72 hours after the extraction is what would be referred to as a dry socket. So, if this high intensity pain you are having began as above (48-72 hours after the extraction, it's what we'd call dry socket.
What should you do? Don't feel bad that you should need to fill a prescription. You are human and pain is real. So, use your judgement, and fill such prescription if needed.
How much longer should this last? While it is ambiguous somewhat to say with any specificity, "generally" two weeks after the extraction, things are "on the mend", as opposed to pain intensifying. So, give it a couple more days, and fill the prescription if desired/needed, but if this pain is not getting better in a couple more days, I'd call your Dentist and have him take a look. It would be rare, but perhaps something is wrong - that needs your Dentist's attention - to get you feeling better.
*Lastly, I'd be rinsing out with warm water every 4 hours or so. Some suggest salt water, and that's fine too, although the water is the important ingredient to cleanse out the possible food debris and all.
I hope this helps you. Please let me know if you have any additional concerns OK?