In the ED, we go by clinical judgment, but the Canadian CT head injury/trauma rule may help guide.
If you are able to read this and write what you wrote at two hours, your GCS (Glasgow coma scale) is 15 - able to speak, open eyes spontaneously and perform volitional motor acts, i.e. normal
If you dont have a palpable or depressed skull fracture or have two black eyes or salty fluid running down your throat or out your nose (basilar skull fracture)
If you have not vomited 2 or more times
If you are less than 65 years old
If you didnt get knocked unconscious, have a seizure upon impact, or have amnesia for accident
If you didnt fall from a height, get struck by a car, or have a dangerous mechanism
Then, do not need a CT scan and you are very unlikely to have a significant closed head injury
If any positives, go to the ED
If you are older, there could be concern for sub-dural hematoma (blood beneath the innermost brain covering and the brain)
If you got struck hard in the temple, you are at risk for epidural hematoma (arterial bleed that is really bad, but if it has been over two hours and youre not comatose by now, this is unlikely.
A brain bruise, or cerebral contusion, happens with dangerous mechanisms, and if identified, buys you a bed overnight in a hospital where neurosurgery is available. The first two may actually require emergent intervention.
I would say that headache is very common, as is dizziness, nausea, spaciness, trouble concentrating, but the fact that you wrote this and are asking makes significant head trauma unlikely (unless youre currently intoxicated).
Theres no problem going to sleep, but if youre really worried, another person around overnight is always a safe thing. If youre really really worried, follow your intuition and get checked out.
Tylenol extra strength (or 3 reg strength) is safest, since Aleve or ibuprofen can inhibit platelets and though not cause bleeding, can make active bleeding worse.