Glycerin could be halal/kosher or haram/non-kosher depending on its source. Glycerin can be derived from both animal and vegetable sources. In skincare, usually vegetable glycerin or synthetic glycerin is used. You can tell it's from vegetable when you see 'vegetable glycerin' in the ingredient list. Another option is to opt for vegan brands to be safe. Even better if it's halal certified ๐ Although not many brands have that and can be hard to find in certain regions.
Besides that, I also avoid collagen and gelatin in skincare unless it is stated that they use marine (fish) or kosher bovine. I avoid sake and wine extracts as well and pay extra attention to fermented skin care. Some are permissible, some are not.