The sound is very feint, almost quiet but when I hear it and concentrate on it, I can't ignore it, it starts overwhelming all sound pretty much
You do the opposite of what you should do, but what probably most of us did when we started to hear a sound in the ear: monitoring the sound, analyzing it, listening to it, concentrating on it, giving it great importance and significance, a recipe for falling apart.
Until and after you see an ENT you should never concentrate on it, always mask it with another sound and do your best to be engaged in absorbing meaningful to you activities all the time, so you forget about this problem, which became so big (a faint sound is ruining your life) became you gave it the central position of your life/brain/attention.
Whether it will remain permanent or will go away, nobody knows at this moment, but in the worst case scenario (if it becomes permanent) you will realize yourself that you don't have to reconfigure your whole life around this faint sound.
Be happy that it isn't worse, there are cases here who woke up with sudden significant hearing loss and huge sound, compared to them your problem is a joke. I really do not want to offend you, but this is a forum with people with chronic loud sounds in the ear(s) and if they have a day when the sound is "faint", the call it "a good day" and all they want is to have as many days like this as possible. So what you are scared of (a faint sound) is their sweetest desire. Or they have different sounds in both ears, and a silent ear will make them so happy.
All you can and should do is to stop this mental obsession, by replacing it all the time with other healthier obsessions.
By concentrating on it you will not make the sound smaller or determine it to go away, but achieve the unwanted opposite, making it louder and embeding it in your consciousness, you will remain with it in mind that you have it (only in silence) even when you are in a noisy environment.
The sound itself is not the problem, it can go away or take a peripheric position in your life, the problem is your reaction to this event, the appearance of a faint sound in one of your ears. Many people get it as they get older, and they continue their life like before, you are probably young, but you must do the same.
Maybe a cause of that sound is identifiable and treatable, and it will go away with treatment or on its own, even it doesn't it's not a tragedy, so do not obsess about it.
I am not scolding you, it's an understandable and human attitude/reaction to this emergence of a sound, but nonetheless very unproductive, wrong, and you must have the opposite attitude. Just ignore this and pretend that you don't have it, thinking about it and listening to it will not cure the sound, nor it will reveal to you its cause. If you can't control this interest that you have for this sound, you can see a private ENT until the insurance kicks in, but beware that many ENT have an unethical attitude and will tell you that there is no treatment and the sound will remain permanent. This is called the Nocebo effect, is the opposite of the Placebo effect and is devastating and a fallacy. It can go away on its own after a short or a long period of time (even years), I know personally some cases. Should it go away on its own, but only in a few years, do you want to have spent all those years as mess? Keep hoping that it will go away one day and you will have your perfect silence again (I perceive you as a perfectionist, which is this situation turn out to be the worst defect), and until then continue to live life you did before the sound, doing the little adjustments necessary (masking when it's audible, if you can't ignore it). You may hate me now, but you will see in the future that I was right.