First cyst and sent away with antibiotics?

I noticed a cyst on Monday and the pains been getting worse till today and so today I went to GP expecting them to drain it and the surgeon at the GP said it can be difficult to get it all out and was sent to A&E

I got to a and e expecting them to drain it and the nurse looked and said it doesn't look super angry just a bit of redness so gave me antibiotics and said if it doesn't improve within 4 days come back

The problem is I'm already in severe pain I can't sit down and it feels like if I could just lance my skin at least it can drain a bit then my plan would be to go and have private laser treatment done as I don't want the invasive op

The nurse was adamant that the antibiotics can make the abscess shrink on its own and relief pressure with hot flannel etc.

Is it true? I desperately just wanted someone to lance it today and nobody seems willing to. She said it's a deep cut to lance it so they tend to want to see if the antibiotics clear it up first.

Anyone had similar experience? Presumably it's going to get worse before it gets better while waiting for antibiotics to kick in and I'm already in severe pain.

What are others experience here?

In in uk