How can I tell my boss how stressed I am without it sounding like I'm incapable of doing my job?

If you are feeling like work is becoming too stressful for you and effective in your mental health, you should try speak too either a supervisor or management team. They should not assume that you are incapable of doing your job role or make you feel like this. They should give you some advice or support in help reducing the level of stress in your workplace. Also could help by reducing the level of pressure causing you stress. It’s ok for work feel stressful at times and you shouldn’t feel like you are unable to get support from management in fear of your capabilities to do the job.