I wouldn't give up! there was a guy on walk trail close to where I live that had some kind of arm or hand surgery  because he ran with his arm in a sling( there was no cast). maybe that is something you could look into doing so it won't throb while you run.

+1 on the previous posts.  It takes time to get over the anesthesia, and it will probably be a few weeks before your arm stops throbbing.  Do what you can, but don't be surprised if it stays hard for a while.  You may be better off doing something like elliptical or stationary bike for a couple weeks, if you have those available.

I had a kidney infection once that required placing a stent between the kidney and the bladder, under general anesthesia. (No cutting, I'll leave the insertion to your imagination.)  A couple weeks later, with the stent still in, "can I run, doc?"  "Sure."  Ha, ha, WRONG!  I was good for about 1/2 mile at a time, when I was routinely running 30 miles a week or more.  It took a while to get it back.

Len

I totally agree with all the other posts. Allow yourself time to get back into it. And I think going back a week or two (or more if that's what feels more comfortable) would be a good idea. As would the suggestion of trying some other exercise for a week or two while your arm recovers a little before getting back into it. From everything I hear, being a runner is as much about mental strength as it is physical, so try to stay positive and refuse to give up. But also listen to what your body is telling you and allow yourself some tim to get back into it A good balance of the two should get you through and still running on the other side of this little obstacle