Unsupervised Text Classification with Python: Kmeans
If you're questions are relatively short and the number of labels are not excessive, I would strongly suggest you take a look at zero-shot classification which can be used to classify data to categories without training a model.
Both multi-class and multi-label classification are possible.
Specifically I recommend using a pre-trained language model such as BART MNLI
You can try it out of the box with some of your questions and labels and see how it works: TRY!
From my experience I think that unsupervised approaches won't give the desired results. So if zero-shot classification is no option for you for whatever reason, I would suggest you try something like snorkel to programmatically build some training data.