Your condition is most likely due a kind of migraine due to vasodilatation of the blood vessels of the scalp and the brain. You may take antihistaminic like Loratidine and non-steroidal anti-inflammatory drug like Ibuprofen for 1 week. (Be sure you do not have any liver problems when taking Ibuprofen).
If no any improvement after a week or at any time you feel any disturbance of vision or any vomiting, you have to see a doctor at once.
Yes, a migraine can be presented with other symptoms WITHOUT any headache. Without some tests and investigations we cannot pinpoint the exact cause of your symptoms. We can also consider the anemia or low blood pressure to had caused your lightheadedness and dizziness. To narrow the possibilities of the cause of your symptoms, checking your blood pressure is one thing to do. Anemia is usually presented with easy fatigability as well as dizziness, try to check your conjunctiva, if it looks pale, then it is an indication of anemia. Checking your hemoglobin count is a reliable test that can tell.
If you are hesitant to see your doctor now, then you may consider my first advise. If you see your conjunctiva is pale, you may start increasing your iron dietary intake. If the symptoms seem to be increasing see, your doctor at once. Above all however, I would still highly advise you to have blood tests done and it would be for your own benefit to get checked by a doctor and find out what rrally is going on.