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