You could bring it up in your doctor's appointment!

Generally, whether you should go to the ER or a different location depends on your location and insurance status. If you're in the US call 1-800-273-TALK to get the National Suicide Prevention Lifeline (website link was given by someone earlier) and your call will be directed to the nearest call center to you. They'll know what resources are in your area and may direct you to a mental health access center or other services without going through the ER. This is absolutely what I would recommend if you lived in my area, especially if you have Medicaid or are uninsured, but I don't know what the centers are like elsewhere.

If you have any fears or anxiety about taking a step like this, try to think of it this way: if you're feeling so crappy that suicide is on your mind, what could really be so bad about trying out emergency help before ending everything? You can't come back from suicide. But SO MANY people, including me, have found relief from seeking out intensive, emergency help.