Hi,
@Tadeusz S,
That is a good question, but I think it's more likely that you have some form of tinnitus than anything else. I have a constant hissing noise, too, but mine is all in my right ear. It is a constant noise, just like you describe, that never really changes. There are many people on this forum who have said they feel that their tinnitus is in their entire head, not just the ears.
Have you had your hearing checked lately? If so, do you know if you have any degree of hearing loss? If it's hissing, I think it's more likely your hearing loss would be in the high range. Gradual hearing loss is a common cause of tinnitus.
Since you've only been to a GP regarding this sound, it might be a good idea to see an ENT or audiologist, to see if they can at least diagnose the problem. There, you could have an audiogram to see if you do have hearing loss. Then, you can decide what forms of treatment (hearing aid/masker, etc.) would be most beneficial to you.
Good luck, and please let us know what you find out.
Best wishes,
Karen