Is it permissible to continue studying medicine at a university that mandates a dress code incompatible with Islamic modest dress (Niqab and Abaya), especially given the significant difficulties and challenges the student faced after transferring to this university, and her feeling of guilt regarding the violation of Islamic law?

If the Shariah conditions for women's dress are met in the coat and trousers, then there is no harm in wearing them. However, if there is another university that does not restrict this type of clothing, that would be better. What happens is not necessarily a result of envy; it could be a test. So be patient and fear your Lord, for Allah does not let the reward of those who do good go to waste. Persist in supplication, for Allah is near and responsive.