I am not a doctor... but if you're feeling that anxious, your GP may well prescribe some anxiety medication to help you get through this rough patch. It never hurts to ask your doctor to refer you urgently, but please bear in mind that pretty much everyone who asks for a referral to a GIC feels just as desperate as you do and all of them want to be seen yesterday.
There are only 7 NHS GICs for adults in England (London, Sheffield, Leeds, Sunderland, Nottingham, Norwich and Exeter) and they all have a lot of patients on their books already, as well as people who are waiting to see them. So the harsh truth is that you're not going to get to a GIC within weeks; that simply doesn't happen in the NHS. It's more like a wait of a couple of months (for the quieter GICs) or even a year or two (for the busier ones). This is due to two reasons: 1) there are far more trans* patients than clinics, and 2) gender dysphoria isn't routinely funded in the NHS, so the GICs have to apply for special funding from your local health authority before they can see you - and like any government bureaucracy, this takes time. So a little patience is required, and if you don't think you can cope with the wait, you need to say this to your GP so that they can try to help you with medication and/or counselling.
Above all, please bear in mind that gender reassignment is a long, slow process that will have lasting effects on the rest of your life. It's a marathon, not a sprint. But your GP - and the NHS - will help you get there. It seems perverse, but GICs are actually wary of people who seem desperate to transition as quickly as possible, because they worry about us making rash decisions. So finding some patience will serve you in the long run.