I've had several. Like anything medical they have to share benefits and risks with you to obtain your consent. Don't forget even paracetamol has a list of scary stuff in the leaflets, but it doesn't affect most people.
Every time it was very calm and relaxed. A bunch of paperwork to go through when you arrive which gives you a chance to settle down and get used to the environment. They take observations (temperature etc) before they start it as a baseline.
When you and they are ready they cannulate you and start the infusion. It's at a steady rate throughout but they check on you more often at the start - it doesn't start slow and then get sped up or anything, it's just that they monitor you more closely at the beginning.
The actual infusion is the quickest part of being there, the paperwork and monitoring before and after take the most time - it's very safe and you will be very well looked after. Having an iron taste in your mouth is the most likely side effect. Every time they check on you they will ask how you feel so you can share any worries and they can reassure.
On one of mine I started to get itchy skin - very very gradually. So they kept a close eye on me and then gave me hydrocortisone and an antihistamine (I forget which one) through the cannula. That took a few seconds to administer and not many minutes later the itching stopped.
Itchiness was the most exciting thing that happened! Now they know my body does that they always give me the extra drugs at the start so we can skip the itchiness. But I didn't have any reaction the first few times and you probably won't either.
Then after the infusion finishes you stay there for a little while so you and they are happy, then they remove the cannula and you can go home.
It might give you a mild tummy ache for a day or so (because it's iron) but then within 3 weeks you should notice you are feeling much more like yourself and you will be glad you did it. It's so much more effective and quicker to benefit you than tablets.
I've also had blood transfusions. I will mention this as you said it had been discussed as a possibility, so you have the info.
If you end up with that later on, it's not as scary as it sounds - they have really careful protocols to keep you safe and ensure the right blood goes to the right person. With a blood transfusion you feel better by the time you go home! But it takes hours per unit of blood so you will be there a long time. Worst bit is getting bored! Iron infusions are super fast by comparison, they just take a few weeks longer for you to feel the benefit.
Do you have any strategies to help with your anxiety? I find focusing on my breathing and talking to myself reassuringly are very helpful in situations like this. Also bringing headphones to listen to favourite music or similar can help as a distraction. If you tell the staff you're anxious they can support you too.
Infusions and transfusions are usually (at least here) handled by a team who do them all day every day - they have it down to an art and they know how to reassure patients because lots of people find it stressful or worrying.
You will be ok and if you need another one in future the second time will be easier because you'll know what to expect and that you can handle it.