No matter where you go or what you’re doing in Belgium, you need to have valid health insurance - it’s a legal requirement. If you are from the EU, EEA or Switzerland, then you will be covered by the state health insurance system from your home country. Remember to bring your (valid) European Health Insurance Card and present it if you ever need to visit the doctor or hospital.
If you are from outside of the EU/EEA, it is still possible that you may be covered by your international health insurance - check with your health insurance provider and ask if they have any agreement in place with Belgium. If so, they will advise you on how to proceed and what documents you may need to provide to ensure your healthcare during the exchange.
Unfortunately, if you aren’t from the EU/EEA and don’t have an agreement with Belgium about mutual healthcare, then you will have to purchase private health insurance from a company in Belgium. Policies start from around €0.50 to €0.89 per day - you can check the details of private health insurance in Belgium to find out what your policy covers, how to apply and so on.
For interns, you may have to subscribe to expat insurance in your home country, since social protection in Belgium may not be available. You should speak to your new employer in Belgium and ask them what to do - they should be able to help immediately, or at least find the answers more quickly than you can.
Your choice of doctor or hospital is not limited by your location or home address, so if you manage to find a doctor who speaks your language or to whom you’ve been recommended by friends or colleagues, you can arrange an appointment with them easily. Always be sure that your health insurance will cover the cost of the appointment and any associated treatment before picking up the phone.