Learn Dutch: Ik ben anderhalf jaar geleden geblesseerd geraakt.

The verb raken is used here as an auxiliary of state change, meaning 'to get' or 'to become'. When used this way, it always uses zijn to form the perfect tense. That is why it is ik ben geraakt and not ik heb geraakt.

Could I say ik ben geblesseerd geworden since worden also means 'to become'?

You will rarely hear that. While worden is the standard passive auxiliary, Dutch strongly prefers raken to describe sudden, accidental, or emotional changes of state, such as getting injured (geblesseerd raken), getting lost (verdwaald raken), or panicking (in paniek raken).

Why are there two past participles (geblesseerd and geraakt) together at the end of the sentence?

Geblesseerd (injured) acts as an adjective describing the state you entered, and geraakt is the past participle of the auxiliary raken (to get). In a main clause in the perfect tense, both get pushed to the end. Unlike modal verbs that trigger a double infinitive, raken allows the descriptive verb to remain a past participle.

Why does anderhalf jaar use the singular form of 'year'?