Can you take a screen shot of that post.

When I look at it with MY profile, I (of course) can see the "Edit Post" option. I need to see what YOU see.

ETA: I've checked out your profile and you have default permissions for everything. Additionally, I verified you have permission to edit your own posts. My guess is your system is glitched. Try clearing your cache and restarting your browser and see if that fixing things. If not, I'll need to know what OS and what browser you're using to try to troubleshoot the issue.