It is most likely that these are blisters, which as you know form when friction and pressure are applied to the skin, causing some layers of the skin to separate and fluid to collect under them. Sometimes, blisters can be 'deep' so that they appear as white spots and not as obvious blebs of skin with fluid under them, and I think this is probably what is going on in your situation.
The first point when dealing with blisters like this is that you should avoid trying to pop them or squeeze them. This does not hasten healing; in fact it may slow healing down. Also, trying to pop them may cause them to become infected.
There are no easy solutions for getting blisters to heal, other than resting and giving it time. It is also helpful to wear comfortable shoes that don't cause any additional rubbing or chafing.
I also suggest that you talk to your primary care doctor
about this. They can take a look at the white spots and confirm that these are just blisters and that there is no need to worry
. They may also recommend a pain medication, like ibuprofen, to help relieve the symptoms.