I had a surgical extraction done a week ago, is it okay to run without worrying about getting dry socket?

Yes but....: You should be ok unless you are running a marathon. It is always best to check with the dentist who removed your tooth as he\she is best able to make that decision based upon your medical history and your particular surgical procedure.

Should be: You should be fine. By now the area should be sufficiently healed that a dry socket is not likely. I would not do endurance , tempo or track for another few days to be on safe side. You may feel "throbbing" or your pulse during the run -- this is normal. Use common sense and stop if anything feels too questionable, or if bleeding starts. Might check with the Oral Surgeon. Good Luck.

After 3-4 days: if you are feeling fine, resume your normal activities. Take care.