Ouch, Rocky - sorry to hear about the injury, but hope you had a good time doing it!
Seriously though, if it isn't swollen or inflamed, then RICE will do nothing to help, as that set up is for sprains (hence the ice) and elevation/ compression (to counteract swelling).
So, do please rest the leg for as long as possible today, and wear either flat or no shoes and be careful going up and down the stairs. Have a warm to hot bath asap today to ease the strain on the Achilles ligament and then massage it very gently and do a few very, very light stretches after another warm/ hot bath tomorrow to try and settle it.
Basically, when the muscle has been overstretched, the connecting tissue seizes up to prevent the muscle from tearing and keeps tightly wound up even after the event - it takes times for it to relax again so heat and careful stretching should encourage it to do so. (I used to be a gymnast and got this a lot with my calves when landing after not warming up enough).
Take it easy, rest and hopefully get better soon
All the best
Peas x