Are there any potential health issues with waking and studying at irregular hours?

It could very well be, as anosmia appears to be a distinctive symptom of COVID-19 infection. In Germany, it has been reported that 2 in 3 confirmed cases have a loss of sense of smell. In South Korea, approximately 30 percent of cases have anosmia as a symptom. You should consult a doctor immediately and inform him of your symptoms. He will take a detailed history and refer you for further investigations, if required. This is even more crucial if you have previous contact history with a COVID-19 positive patient.

It depends on whether you have travelled anywhere recently or if you have any positive contact history. If your answer is no, you may still visit your GP or the nearest PHPC clinic. The A&E is best reserved for emergency cases, especially in a pandemic.