To be able to say if it's something that might be possible for you - we'd really need to see your audiogram, know how well you understand in noisy environments, etc. All these things come into play ...
Do you have a recent audiogram (or one that accurately represents your current hearing loss).
Without that, here's my 2 cents.
IF you are able to hear and understand well in fairly noise environments it may be possible to become an interpreter as long as you voluntarily restrict yourself to certain types of jobs such as:
*Doctors appointments (where you are interpreting for a dr/nurse and the client in a quite office)
*Certain school/university class settings (will depend on the acoustics of the classroom, the noise level of the class etc
*Smaller sized Churches/Synagogues/Mosques, provided they have good acoustics (in this setting most of what is to be interpreted is a "known material" ie written liturgy/song lyrics that you can learn advance, and often sermon notes and announcements that you can request in writing ahead of time - making it easier to fill in any "gaps" you may have when listening to what is being said "live" and interpreting it, since you'd already be familiar with the material being spoken/sung etc)
*Interpreting for some types of meetings (ie parent teacher interviews, job interviews etc) provided they take place in a quiet room with little background noise.
and similar type situations ...
I'd recommend NOT taking jobs that are in larger rooms with more than 30-40people in the room (ie conventions/conferences, sports events, Political election gatherings etc) or places like hospital ERs which are often noisy and the information HAS to be transmitted perfectly as a matter of life or death. These situations due to the physical spaces (acoustics) as well as the amount of people/nature of the gathering/room/area etc will almost always mean a lot of background noise, which is often challeging for HEARING interpreters, let alone anyone with even
slight hearing loss. These are the situations in which you will have the greatest "risk" of not being able to provide the level of service the clients needs, and deserves - as such the only responsible thing (as I see it) would be not to take those type of jobs.
The other option, as Botts & AlleyCat mentioned is studying to become a CDI - certified Deaf interpreter (versus a Certified Interpreter FOR the Deaf). This may be easier for someone who has a native (or near native) knowledge of ASL (or some signed language), but it is certainly possible to acquire the skills needed through lots of hard work for those without a native knowledge of a signed language. The advantage of studying for a CDI instead of a ASL/English (hearing) interpreter is that a CDI may be (and often is) Hoh or Deaf themselves - this means that if something should happen that your hearing changes over time, you'd still be secure in your job - whereas if you were a "standard" ASL/English interpreter you'd almost certainly be unable to work (and have to re-train at that time either as a CDI or a completely different career.)
Here is a description of what a CDI is, and does from terpslink.net
A Certified Deaf Interpreter (CDI) is an individual who is deaf or hard of hearing and has been certified by the Registry of Interpreters for the Deaf as an interpreter. Specialized training and/or experience In addition to excellent general communication skills and general interpreter training, the CDI may also have specialized training and/or experience in use of gesture, mime, props, drawings and other tools to enhance communication. The CDI has an extensive knowledge and understanding of deafness, the deaf community, and/or Deaf culture which combined with excellent communication skills, can bring added expertise into both routine and uniquely difficult interpreting situations. Meeting special communication challenges A Certified Deaf Interpreter may be needed when the communication mode of a deaf consumer is so unique that it cannot be adequately accessed by interpreters who are hearing.