Need some advice
 

I broke the lug nut off when changing a flat. There is still part of the lug nut but not enough to grip or anything. I was told to drill it so I did. Here is where I am at now. Still wont break free. Any tips?
Attachment 820

Can you drive this to anywhere? I would recommend you get a good mechanic to drop by with his tools and try to do it himself. This doesn't look safe if you've never done it before.

was your plan to keep the wheel ?

Drill it clean can surely remove it, unless you have no plans of keeping the way a blow torch will surely be handly.

I had that happen on my civic and I just ditched my wheel. Again, To reiterate what was already said, go to a mechanic if you're unsure how to do it.

limitation of car tires

I would recommend you get a good mechanic