I'm not sure physically where you are, OP.
In NHS Scotland there are Primary Care Mental Health Services (PCMHT), which see people with mild to moderate mental health concerns. These are self or GP or other professional referral. I believe in England the service is called IAPT.
They will typically decline people who are actively suicidal as they do not have an out of hours/"duty" team. This means that if you need them not between 9-5, they can't respond.
For people experiencing suicidal ideation or more severe mental ill health, there is the Community Mental Health Team (CMHT). This needs a referral from a professional eg GP. The referral must mention that you are suicidal and outline your mental health symptoms properly. These teams have out of hours /duty teams attached.
I would suggest you go back to the GP and ask for a referral to secondary mental health care/CMHT equivalent. Outline all your symptoms as honestly as you can (write them down and hand it to GP if that would be easier).
There will be a wait for services. If you have a secondary mental health referral you can usually contact them if you feel suicidal, even if you don't have a professional allocated yet. Id also recommend you have a "keeping safe" plan for yourself that includes numbers for charity services (breathing space, Samaritans etc) and for a trusted loved one you can speak to.
I'm not sure exactly what mental health symptoms you are struggling with outside suicidality, but it's also worth getting vitamin and thyroid levels checked; checking hormones (particularly if you are a woman towards peri or menopausal age), taking vitamin D and eating as well as you can (regular meals). This is because some vitamin deficiency, hormone problems and thyroid problems cause low mood and/or anxiety. Try to get outside every day if you can, even for 5 minutes. Schedule in some activities every week - ideally some social things and some physical activity. If sleep is a problem, work on sleep hygiene and free tools to improve it (for example sleepio app if you have insomnia).
These things are so hard when you are struggling with mental health but they are the building blocks of good mental health.
Wishing you all the best - your mental health matters, you matter.