Personally, I think it is normal. Your body is changing. I feel dizzy all of the sudden too and feel nauseous. But if it is something that worries you see a doctor. I've seen a doctor 3 times already just because I wanted to confirm everything is well. If it is your first time pregnancy the doctors office will understand if you, call them and leave a message :-)
Make sure you are getting enough iron and protein as well as a lot of water! That should help with the dizziness! But if you are feeling it often, I would definitely mention it to your OB or midwife!!