Does it happen every time? If I masturbated too much in a short period my penis would be sore when I got hard again, but it didn't hurt, or was painful. How quickly are you becoming erect again?

It's normal for it to be extra sensitive a bit sore during the "refractory period", and this is especially noticeable if you get hard again soon after. It shouldn't be outright painful, but a little soreness or ache I'd say is normal (at least for me).

It is definitely sensitive after cumming and that can mean continuing to stroke it as you were before cumming would be painful but I accommodate that by not stroking like that. Sometimes I give a few gentle strokes but I am also uncut so there is no direct contact on the head.

Normally, that sensitivity should have gone away again by the next time you get hard. It is hasn't, have you perhaps been a bit too rough? Also are you cut/uncut? If uncut, have you maybe overstretched your foreskin?

don't know what refractory means, but I know that if ya do something too much its not good

• refractory periid is the recovery time between ejaculations
  

I know what it is but have always thought it was a strange word, so I looked it up. The relevant meaning here is "resistant to a process or stimulus." It is usually defined as the period between cumming and being able to get hard again.
Ok, next question: does your foreskin slide back easily? If not, it maybe that you're being sufficiently gentle with it at first but then, as you get close, get a bit more enthusiastic and pull it back a bit further than it wants to go, putting microscopic tears in it.

It’s pretty normal, at least for me. When I jerk off I usually “edge” meaning I stroke for a while so that does create some soreness.