If you want to try collagen supplementation, you certainly can, though the scientific evidence is a bit of a mixed bag. Some studies seem to show benefit, but I think we have to keep in mind this condition is also a temporary issue brought on by the stress and dietary deficiencies you went through. In short, it's going to resolve by itself over time and thus it's really hard to know if the collagen is actually doing anything.
IMO, the best possible thing you can do for your health, for your hair loss, as well as to speed your weight loss would be to really double down on dietary protein intake and not supplements.
For those about to jump in and mention that collagen IS protein, yes that's true, but it does not contain all the essential amino acids. As such, you really should not count it toward your daily protein intake. Plus, a capsule isn't going to contain very much protein anyway. I'd guess less than a gram per capsule, though I suspect it might vary based on the source and size of the capsule itself.