Oh my goodness, that sounds terrible! I'm not aware of anyone having similar issues, but I'll ask a few of my colleagues and see if they have any insight, or knowledge of this happening before.  I do know, from personal experience, that those types of wounds are indeed painful. 

There is no specific reason for your response. By that I mean that Yuccas do not contain any particular substances/poisons that universally cause reactions like yours. Perhaps you are allergic, and I suppose there's potential from some outside substance that happened to be on the surface of the plant at the time that it punctured your skin, but I have never heard of such a problem. 
I'll keep your question open and get back to you once I have gathered some additional information.

I received a lot of feedback from colleagues who have experience with this issue:

Many suspected that a tiny, even microscopic, shard of plant material had been left behind and would need to be extracted before you would receive any relief or begin to heal.

Others listed experience with an external contaminant that caused an infection such as tetanus or staph. So your antibiotic treatment should assist with that possibility.

Another suggestion was allergic reaction to the plant sap.

And lastly one colleague suggested than an outside possibility might be plant thorn synovitis. More inforamation here:
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2628235/
http://www.medicinenet.com/plant_thorn_synovitis/article.htm
The above two links are not to Extension resources, so I can't vouch for them, but they may give you a starting point for discussion with your physician, if necessary. 

I certainly hope that you are healed already! Since this message took so long to get sorted through our system. My sincere apologies about that.