My arms hurt after doing too many pushups...what am I doing wrong?

I'm trying to get myself back in shape for when I join the Navy. I haven't worked out in a really long time and just recently started back up about a week or 2 ago. Yesterday I did close to 80 pushups at once and now I have this crazy pain in the back of my arms where my triceps are. I'm trying to lose fat&gain muscle but I can't really continue when I have to deal with all this pain. It's gotten to the point where it's very uncomfortable for me to do anything. I don't know what I'm doing wrong.
My arms hurt after doing too many pushups...what am I doing wrong?
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