To fight for a GP appointment tomorrow?

[Infernalhellloop]

For a week I've had a blocked nose, coughing, producing literally buckets of dark green khaki mucus that is lumpy, thick, sticky generally yuck.

Doesn't seem to be getting better. Had one day improvement then back to no improvement.

Now feeling light headed/ dizzy.

Ulcers on roof of mouth from mouth breathing due to snot build up.

I'm super run down.

Do I need antibiotics or should I put up with it for longer, I feel awful. I've had antibiotics for chest infections before this time I've not sought any medical help as of yet?

Well I've been a GP for over 20years and have seen many thousands of chesty coughs and I assure you the VAST majority are viral and don't respond to abiotics and can take weeks to settle. But people want a quick fix for everything.
So I would say I am far better qualified to offer a general opinion than some randomer...

In general, yes, but for specific cases unless they walk into your practice then no. My chesty and productive cough absolutely needed antibiotics according to the NP i saw.

Sure

Sounds like a sinus infection to me. I tend to get them after a cold
Just finished antibiotics for them. Have a look on the NHS app and log in you might be able to book a telephone appointment with your gp on there. That's what I did.