Short answer: the iron goes to work over several weeks. How fast people notice a change varies a lot.
The first few days
Some people feel tired, achy or have a headache. Rest, drink water, and see "When should I call after an iron infusion?" for the signs that need a call.
The next few weeks
Your body uses the new iron to make red blood cells and refill its stores. Changes tend to be gradual, with good days and tired days along the way.
Why your next blood test waits
Ferritin rises for a while right after an infusion, so an early test can look higher than your real level. Doctors usually recheck several weeks later. Your doctor will tell you when.
What helps
Write down how you feel each week. It gives your doctor more to go on than one blood test.