Is it possible to exhaust all possible local options if I fail too many interviews?
Theoretically this might happen. However for most kinds of jobs it's unlikely.
At one extreme, supposed you want to be a firefighter. You apply, and they decide you would not make a good firefighter. It won't matter how many more times you apply you won't get that job, until something has changed in terms of your training, experience, or other qualities. You've now exhausted all the employers who might hire firefighters. (OK, maybe there are two fire departments in your area, or you can get a job in a related field.) However just because you interviewed and didn't get the job that doesn't mean they didn't think you would make a good firefighter. Maybe they only had one position, and you were the second best application. Next month another position comes open and this time you are the best application.
At the other end of the scale, software developers (for example) comes in lots of different kinds. A company may turn you down because you don't have enough database experience for the role they are hiring for. Their next position may need Python skills and no DB. You might be perfect for the role. So even being turned down by a company doesn't mean you won't be hired next time. On the other hand, if they think you are a bad developer they will still turn you down in future interviews. This is especially true of companies that like to hire on "overall aptitude" rather than specific skills.
For most job types, the recruitment market is always flexible. There is always a new company looking to hire software developers. Or a company changes the kind of developer it is looking for. And there may be a company you have never heard of that hires rarely, but suddenly starts to look for people like you.
Sometimes I'm afraid to apply for a job at a good company locally as if I fail I might not have another opportunity at that company to interview.
That's not an attitude that will help you. Failing an interview doesn't mean you will never pass an interview with that company again, if their requirements change. If you would fail so badly that they will never consider looking at you again, then you are probably going to fail that interview in six months, or a year. The number of companies that hold grudges like that is very small.