Seeing a doctor to be sure is a good idea, for your own piece of mind I guess.
I've been competing as an amateur boxer for about 3 years now, and training for much longer. What you describe happens quite frequently, and you shouldn't be alarmed. When your technique improves you will be able to roll with the punches much better and this feeling you have now will happen very rarely, if ever.
I spar nearly every week, at a variety of intensities, and from time to time (maybe every 6 months or so) I get a slight headache after training. As long as you are not dizzy, nauseous, or otherwise heavily impaired it's nothing to worry about. Like any other sport, your body needs time to adapt to the rigors of your training.
If you haven't already, invest in a good headgear. The best you can possibly afford. It is the single most important piece of equipment you need, 2nd would be a mouthguard.
See a doctor if you want to be sure, but don't worry too much- it gets easier with time spent in the ring. Keep your hands up and your chin down!