Hi,
we only help with unemployment insurance – and therefore we can not help you with healthcare related questions.
However according to Lifeindenmark.dk:
https://lifeindenmark.borger.dk/working/cross-border-commuters/cross-border-worker-and-health-insurance
„As a cross-border worker you have access to medical treatment both in your country of residence and country of employment (Denmark). That means you can choose whether you want to use the healthcare services in your country of residence or in Denmark.‟
You can also find more information at https://www.pendlerinfo.org/pendlerinfo/dk/.
Remember when you work in Denmark you must be insured againt Unemployment in Denmark. So if you not already have done that, you must sign up with an A-kasse in Denmark.
Hope it helps.
Best regards,
Anders Weber, A-kasser.dk