thanks for posting your query,
I am so sorry for your troubles and I understand it must really be difficult dealing with such a situation.
How ever, it is possible that the antibiotics given might not be effective against the causative microbes causing the burning sensation you are feeling. This could either be because of resistance or that it might be an atypical germ causing the infection.
So saying, you might require a urine analysis plus culture to actually isolate the germ responsible.
Also the rashes you are having at the vulva
of your vagina might be due to fungi or even bacteria. Also, some rare causes of UTI can be yeast infection which needs to be treated specifically with antifungi medication.
So saying, you need to revisit your doctor who may decide to place you directly on another treatment option or first run another urine tests before proceeding with given you treatment. Also needs to confirm that the rash you are having is actually caused by fungi before prescribing a cream such as miconazole
or ketokonazole cream etc to deal with this infection.
Hope this helps and wish you the best.