@LemonadeLocomotive - 'normal' haemoglobin range depends on phase of pregnancy. Should be above 110 in first trimester. Above 105 in second/ third. They generally will prescribe iron if near those limits. On iron, you should expect hb to rise by about 2 per week.
Ferritin levels are a separate blood test and not always performed. Basically, most people's ferritin will fall before hb as it is the 'store' of iron that you've got. Generally ferritin below 30 is considered abnormal and anaemic, regardless of hb level.
They will always prescribe iron before trying an infusion. If hb levels don't rise on the first iron tablet, they will have you try different tablets and will do almost anything to avoid doing infusions.
The reason I suggested having that discussion of below 95 is because op may not have TIME to get her hb levels up before she delivers because she is 37 weeks. Anaemia during birth leads to increased risks... so to avoid these, need to not be anaemic ASAP!! An iron infusion would do that.
If she were, say 30 weeks, should would have a bit of time to try tablets to improve the anaemia.
They will generally consider a blood transfusion if hb below 70. My hb was 73 after dd's birth. So they were like 'here are your tablets. Off you go!'
But guidelines are different everywhere. Choices made about treatment are based on symptoms AND tests. One person might feel absolutely shit with hb of 110. Others it might take hb 90 for them to feel the same levels of shitness...