Chicken and fish have v little iron, hence veggies struggle (if you're not veggies red meat will be much better for you).
Theres no reason not to give you an iron transfusion, if they have evidence of tried supplementation, but the service is super stretched so you're far better approaching the consultants secretary in a friendly manner and explaining your symptoms that you're struggling with and suggesting they consider allowing an iron infusion rather than demanding one.
Please don't approach them in the manner of "I'm getting an iron infusion one way or another" as you'll just get the backs up of the people you need to help you out (such demanding statements from patients are really irritating, as with years of medical experience theres lots of things we need to take into consideration, and don't take too kindly to demands (regardless of whether they're correct in their reasoning or not), be friendly it will get you much further.
I regularly go to beg for expedited infusions on my patients behalf (to multiple different teams and managers involved) before surgery, but that's me going above and beyond, which people are less likely to do if not asked nicely, if someone's demanding you're more likely t9 just be put on the routine waiting list than potentially fast tracked
Other things to consider are b12 and folate levels which both contribute to anaemia and are v common in both veggies and IBD (more so with UC than crohns but both can get it)