Please, please, please, do not run with a painful Achille tendon.
Now I am recovering from the Achille tendon operation I had 2 months ago.
I was stupid enough to make the same mistake you want to make now.
The price for running now could simply be throwing away you future long term running health and fitness. Is a race now worthed several months or years of future running ?
I would not wish my worst enemy the long term consequence of running with a painful Achille tendon.
Please, be wiser than I was.