After a while of taking my gonorrhoea drugs I began feeling this burning sensation on my tongue and its white.

Yeast infection. Yeast infection / overgrowth can occur, when one is on long term antibiotics and the "good" bacteria are destroyed along with the bad bacteria. See the doctor who prescribed your medication to determine if a change in drugs needs to be made and to treat your tongue infection. It is often beneficial to take probiotics or eat yogurt w/ active cultures about 2 hours after each antibiotic dose.
Possibly Candida. It is not uncommon to develop an oral yeast infection after a bout of antibiotics. To be sure that is what is(& not something else) and for treatment you should see the doctor who gave you the antibiotics, an oral surgeon, or dds to evaluate properly.