I don't think all psychological problems necessarily rise to the level of "mental illness." It's just not true that, if a person's mind isn't functioning perfectly, the person must be considered to have a psychiatric disability. I think we have to leave room for a grey area between between being outstandingly fit, physically or mentally, and being "diseased." You are holding down a job. You must be an asset at the animal rescue facility, or they would have let you go. But you sense that you are not "hitting on all cylinders," as the saying goes. It's healthy that you recognize that.

Your mind is not fully on the activities of your daily life, possibly because you have some important need that isn't being met. Your mind may be telling you that there is something that needs attending to, outside of the things you are currently trying to take care of. I wouldn't call that "mental illness." But it may be time to take stock of where you are at and what aspect of your life needs more attention.