This may not be tendonitis - you may have stressed/bruised your OC calcaneous!
This horrible sounding thing is the ball of bone directly under your heel. Any new activity can change the way your heel strikes the ground and any change can stress the OC. So new trainers may not have the same amount of cushioning in the same places, and could cause such stress.
It is also possible that the pain coincides with the new shoes. If you have ben increasing your activity levels, or started doing something new then your body may not be responding as comforatbly as you might like. Such pain and stress is a very quick way for your body to get you to stop!
Most importantly though is that this little bone is one of the first indicators of osteoporosis. Radiographers often look here for early signs for ealry signs known as ostepenia (bone thinning rather than loss, is one way to think of this). But radiography isn't the only way to tell, your GP could ahve as accurate an diagnosis from your family and personal medical history!
But don't panic. Osteopenia is reversible with a diet and drugs regimen and can result in better bone health in even the oldest of patients.
Now I don't know your age or medical background but, if you were a client of mine, I would be advising that if this pain continues then you should see your GP and ask about ostepenia as a cause. Test and treatment are quite routine and should prove no problem for any doctor.
I hope that this doesn't scare you but informs you that such pain is your body's only way of letting you know that it needs you to change a behaviour! Run less, skip less, take in more calcium, start HRT - whatever!
Good luck, I hope it stops hurting soon!