Dentist recommendation for toothache

I've been experiencing a toothache on my lower left side for a while now. It first started in early April, and while I was in Bosnia mid-month, I went to see a dentist there. They took an X-ray and told me it was two teeth squeezing too closely together, causing infections. I was prescribed Amoxicillin, which I took for a few days, and the pain went away.

However, the pain started up again last week and I am now out of Amoxicillin. I called 111, but the experience was so frustrating that I’m now open to seeing a private dentist instead. I’m flying out of UK later this month, so I can’t do any long-term treatment, but I’m in urgent need of an emergency assessment or a toothache-specific appointment.

Any recommendations for specific clinics or dentists would be greatly appreciated!