A CT scan and spinal fluid analysis are sufficient for excluding a subarachnoid bleed. You do not mention if there was 'xanthochromia' in the CSF sample, an important thing to look for in exlcuding a bleed. Depending on your physicians suspicion, they could do a CT angiogram if one is available in your area to exclude an aneurysm. This is just a new generation of CT scan with som edye that is replacing invasive needle angiograms for aneurysms.
If you have risk factors for a blood clot like history or family history of blood clots, smoking, being on the oral contraceptive pill, they may need to exlude a venous clot in teh brain by doing an MR venogram.
New onset severe headache which persists (especially if you are over 40 years old) makes an argument for getting an MRI of the brain which provided much more detail than a CT (although generally not as good as CT for blood).
Good luck
It is possible to have traces of blood in your spinal tap. Sometimes the doctor doing it can make an oops and cause you grief. My son had such headaches and they lasted forever. Check everything out like I did and later we found out it was lyme disease. Little did I know that headaches were the first sign of it for him. His pain is on the left side of his head in the back. Don't stop with the doctors until you get some answers, it takes time!