Swollen tonsil with white patch

Hi, 

5 weeks ago I had pain in left side of throat. Only when swallowing sometimes or oddly when I laughed. Sometimes drinking water helped me, as if my throat was dry and sticking. The pain passed but I have noticed my left tonsil is swollen and a white patch just above tonsil, about size of 5p.

I've tried getting a doctors app but have been unsuccessful. Doctor rung me today and ask some questions and for me to email a picture of throat. He rung back and said he can see swelling and looks like an infection but because there is no pain, doubted it was and said unless it swells, causes pain or becomes raised, its nothing to be concerned about but didn't know what it is. 

Bit concerned with what it is and what to do next, seeing as I don't had it for 5 weeks.

Scared it could be serious and if left could get worse.  

Tia.