Your symptoms point towards a very common problem called Plantar Fascitis.
This is swelling of the fascia covering the muscles under the foot.
The tender area which you feel at the centre is the attachment of the muscle to the bone. This is most strained when you stretch the foot.
Treatment is as follows:
1) Anti inflammatory medicine like Nucoxia 60 twice daily.
2) contrast bath to your foot.
3) Ultrasonic heat therapy
to the area by a physiotherapist.
4) wearing soft sole footwear
5) Foot stretching exercises
6) wearing night dorsiflexion
splints on your foot while sleeping.