You need to drink pints and pints of water for the next couple of days. A urinary tract infection or concentrated urine can cause these symptoms by irritating the bladder wall. By drinking the water you will dilute the urine and flush away the irritation. If you develop lower back pain, temperature or there is no improvement after the weekend then I would like you to see your doctor. Also I would suggest avoiding alcohol in the meantime too.
That is related to the symtoms of cystitis, at your age then it is unlikely to be anything more sinister. Cystitis causes pain when passing urine, and a desire to empty the bladder when there is nothing to pass, this is due to stimulation of the blader wall muscle from the concentated urine. If it were to continue for a long time, or you were older then I would want other investigations but at the moment then I would treat as simple cystitis.
Yes, if the urine stings excessively when passed you can ask your pharmacist for potassium or sodium citrate sachets but water is the best thing to do at home. Give it 24-48 hours and if there is no improvement or you develop a temperature then see your doctor in that situation.