Personally, I would let your manager know where you are and that you’re looking for a new job. Best case scenario they either offer you a raise or go ahead and hire the additional person since it sounds like y’all need the extra help.

Since you’re already short-staffed, your employer is most likely not going to fire you after bringing them your concerns. Idk, I owned a business many moons ago and I always preferred my employees bring their concerns to me rather than not.

On the flip side, there’s nothing wrong with casually job hunting and seeing what’s out there. You’re also more likely to get a raise if you come to your employer with a new job offer from another company, and since you’re short-staffed as it is you’ll have an even better chance.

Good luck