I would not worry about it....Rest a few days..Ice things down a little ben-gay or icy hot...plenty of hot baths...

As long as you feel no head trauma..headaches,,blurred vision dizziness,, nauseous ect...If you feel any of that see a doctor and DON'T SPAR UNTIL YOU DO!!!

Could be a few of these reasons for the body pain....

1 you did not feel any pain while sparring because adreneline and anxiousness were keeping you pumped up...BUT....Those same nerves and adreneline can keep muscles tight without realizing it and tight muscles when hit on once relaxed feel the effects more....

2. You may just not be used to the sparring and getting hit....EG-- if you have a job in an office and one day go out and do blacktoping you use muscles you do not on a regular basis...So the next day you are sore

3. Try to spar at a lighter pace...Maybe the guy you sparred with took a bit of liberty ( don't know this for sure just offering intput)...When you spar you need to get used to things..start slow...no need to hit hard...remember sparring is for learning......I have seen guys who could have been great fighters but left their best stuff in the gym during what is called gym wars...feed the macho side...some guys like taking advantage of guys with less experience makes them feel top of the food chain at the gym....

4. Don't workout after sparring...do your workout before sparring then after sparring just cool down...EG after sparring do not just sit and try to recoup...jump a little rope..pace back and forth shake out the muscles so you cool down slow and muscles dont get tight.Just like you stretch and warm up before working out to avoid injury same goes for after working out.....

If the dizzy feeling does not go away see a doctor asap...

hope some of this helped