Yes antibiotics need a prescription here in the UK. Do you have any other vets near to you? What area are you in as I have a list of poultry friendly vets in my practical poultry magazine.
Hi :welcome
Glad you could join us here! Your chick is a polish and they can suffer eye problems due to their crest. Sticky eyes can sometimes indicate a respiratory problem which could be causing the lethargy. If it's resp infection the only way to treat is with antibiotics if they can't fight...