I'm 45 and had recently a sudden hearing loss, at right only. The consequence is a difficulty to mix instruments and have a good stereo balance.
Sorry to hear.
I work in a hearing clinic and have seen several individuals with sudden sensorineural hearing loss in one ear. Often the cause is unknown (ideopathic), but attributed to viral infection of the inner ear. Other things can cause sudden changes in hearing, such as...
I recently had a barotrauma event while scuba diving and will be in the same boat
...but in this case the cause is known.
Noise-related hearing damage is anther things to be aware of (when using machinery, or listening to music at loud levels for extended periods of time, etc.)
I think I have to mix only on headphones and apply an EQ at right to compensate my lost frequencies...Then, how to EQ ? I fear to boost too much the lost frequencies and the frequencies around them.
In principle, what you are describing is how hearing aids are set up to accommodate for a hearing loss; however, they are designed specifically for this (and also include compression with multiple knee points, limiting and individual settings across multiple frequency bands). What you are describing may be possible with headphones depending on the degree of loss; however, if the degree of loss is great, you may be boosting quite a bit and causing distortion in the transducer as a result. Something like Cubase's Control Room allows you to put an EQ in the monitoring path, for example.
Also, the residual hearing you have after a hearing loss means there is smaller dynamic range you have to work with. What I mean is that if you arbitrarily picture hearing ability from 0-100, if you lose hearing (now your hearing is from 40-100) your overall range has decreased as the maximum loudness you can tolerate does not move (it is still 100). The practical effect of this is that you are squeezing the sensation of "soft", "medium" and "loud" into a smaller dynamic range, so it will feel a bit different that having full-range typical hearing.
But I don't know how to establish a precise and reliable audiogram (the one done by my doctor is not precise). Is there a good plugin out there ?
Audiograms are pretty standardized, but they are relatively coarse and band-limited, as least with respect to the frequency range you will find in music.
Standard hearing-test frequencies are (in Hz): 250, 500, 750, 1000, 2000, 3000, 4000, 6000, 8000
Some clinics will have ultra-high-frequency testing that extends to ~18000 Hz, but most clinics will not do that at is has no real utility when working with hearing aids. Keep in mind that hearing clinics are focused primarily on communication, which is largely encompassed in the range of frequencies outlined above. I have never personally seen anyone test lower than 250 Hz
Standard difficulties that accompany unilateral hearing losses are (a) localization of sound, as interaural time and amplitude cues are thrown off due to the imbalance between the ears, (b) listening in the presence of background noise, as the brain has a natural ability (referred to as "binaural squelch") that helps suppress noise when receiving signal from both ears.
As an aside, I would recommend anyone experiencing a sudden loss of hearing to treat it as an emergency. Often emergency departments or otolaryngologists (Ear Nose and Throat specialists, aka ENTs) will have a sudden-sensorineural-hearing-loss protocol which involves steroid injection (through the eardrum). The window to treat this is quite small, so the sooner you look into it the better chance you have of recovering some degree of hearing, though there is often some hearing loss that remains. It is a bit hit or miss as to how effective this type of treatment will be, but the sooner the better in most cases.