The basic rule is: In an emergency, you will be treated in Germany in any case. It is best to go directly to a hospital or call the emergency number 112.
All persons who have their residence in Germany must have health insurance. Your arrival centre/state reception centre or the social welfare office of your place of residence will make sure you get a health insurance. Ukrainians who wish to study here are not exempt from this obligation.
If you do not (yet) have a health insurance, you can get bridging benefits from the social welfare office, which include medical care. Before you go to see a doctor, the social welfare office (Sozialamt) must issue you with a treatment certificate.
In some cities there are also organisations that treat people free of charge and anonymously, e.g. Malteser Medizin or Caritas. It is best to clarify the opening hours in advance.
By the way, you can also get vaccinated against Corona free of charge in Germany.
Further information on medical care, also in Ukrainian, can be found at germany4ukraine.de.
Proof for universities
By the way: All persons who wish to study in Germany must present proof of health insurance when enrolling. Ukrainians who wish to study here are in principle also subject to compulsory insurance in the statutory health insurance scheme as a result of enrolment. You will receive more detailed information on this topic from the providers of statutory health insurance.