Is it possible to still have low iron stores without periods?

[rabbitfacts.livejournal.com]

Hello, I hope this is okay to post this here!

I went for a blood test for an unrelated problem recently and it's come back that I have low iron stores and I need a top up of ferritin. I'm slightly confused though as my last two periods have been literally so light that they've barely been existent and only have lasted around 2 days. Is it possible to still have low iron stores even if you don't have heavy periods? I've also been trying to eat more red meat in my diet (more than I used to in the past) so it's very bewildering.

I was hoping someone might be able to shed some light on what I can do in this situation so if anyone has any advice for me on the following questions I'd really appreciate it!

Can low iron stores still occur without periods or on light periods?
Is there any way of building up my iron without taking iron supplements/pills? I suffer from very severe constipation and am absolutely terrified of taking them in case it causes problems.
Is there any way to potentially help absorb any iron I do have or any food I eat that will benefit me?

Thank you!!