Pain in the back of Heel

...also your saddle height may need adjustment. I set my bike up with trial and error, and at one point moving my cleats a matter of millimetres alleviated knee pain! However a proper bike-fit is advisable.

Also, think back - did you do any other activity that day - the delay in getting the symptoms suggest it could be something else that caused it. My most annoying little injuries tend to come from stupid things like paying with the kids!

If there is no rubbing from the shoe whilst riding, it is most likely that the cleat position needs to move nearer to the heel. You might be over stretching the achilles. Be careful you don't exacerbate the issue. Pull back your cycling and adjust cleats. Even have rest off the bike to let the heel issue settle down.

Have you gone straight into long rides on the new pedals? - the fact that clipless pedals allow a much better range of motion and also allow (and encourage) effort throughout the rotation, means that you may have strained your achilles. Rest, and then gentle re-introduction would fix this.

Or, you may need to play about with your cleat positioning - a full bike fit would be the best solution to this.