Am I allowed to drink a juice made from dried insects, for medicinal purposes?

With reference to your query, please be informed as follows:

Consumption of Insects is generally regarded as impermissible, grasshoppers are an exception to this. [Nawawī, Majmūʿ]

However, as a rule, consuming anything impermissible, may be regarded as permissible when considering the following:

When consumed in extenuating circumstances, such as extreme famine [Nawawī, Majmūʿ];

For medicinal purposes, while alternative [permissible] medication is not at one’s disposal. [Nawawī, Majmūʿ]

As such, drinking juice from dried insects is only regarded as permissible, when there is no medication that is equally or more effective at one’s disposal.

والله تعالى أعلم

And Allah knows best.