Any advice on what I should do in this situation.
I really need to get rid of this health problem until university starts, I have plans on joining a sports society etc, which is going to be near impossible with this rash...
Are you getting any help for your anxiety? If you're not, please look into it. Unfortunately, your GP is right, there are certain threshholds you have to meet to be referred to allergists/dermatologists. What medication have you tried? What doses? Might be worth asking your GP about specifics. I'm on quite a high doses of various anti-histamines (prescribed that way by my allergist/dermatologist) for my issues, some of which sounds similar to yours.
I have tried different doses of different medication, unfortunately I don't remember which ones exactly but I definitely tried "Fexofenadine", I have also tried to take them at different times e.g. before the rash, during and after. Nothing had a positive effect . I am not a fan of consuming medication for a long period of time, If I don't see any positive results with in couple of weeks I will stop because it seems useless to spend money and drug yourself if you don't see results. Not exactly sure how exactly I can get help with anxiety, Advice on the internet seems very pointless, and some of them like "express your anxiety to people around you", will only cause more anxiety in the end.
Can't speak to private care though, I didn't go down that route.