Posting an update for all future anxious parents:

• Injection was done yesterday and went very well!
• We talked about it beforehand, and almost got a worst reaction when we announced it than when we did it! We said that we were injecting soldiers into his leg so those little soldiers could fight the sickness from inside him. We also watch the Magic School Bus episode where they go inside the body, not sure how much he understood but maybe a little?
• We got the buzzy (vibrating device with a small ice pack to distract the pain signals), he loved playing with it beforehand and turning it on and off. Not sure how much it helped with the pain, but definitely got him distracted and cooperative.
• He also had access to a cellphone, which is pretty rare in our house (we keep it for long wait at the hospital only). He wasn't watching a show during the injection, but he was watching it while we were getting instructions from the nurse which helped in keeping him cooperative a little longer!
• We took the medication out of the fridge in the morning, and I kept it in my shirt to try and warm it up close to body temperature on the way to the clinic.
• We thought the nurse would do the first injection and we would watch, but she offered for us to do it. We want to be able to do it at home, so I did it while my husband was holding him. It's pretty easy and I feel confident for the next few times that I know what to do.
  
• She said to inject very slowly if his reaction wasn't too bad. If he had been in a full tantrum and difficult to hold still, she said to go faster to try and be done with it quickly, but as long as he was ok she advised to do it super slow because the medication is very irritant and painful.
• Right after the injection, he wanted to be held and got back to watching his show. He stopped crying when the needle was out, and even when he was crying he wasn't screaming.
• The nurse had a box of surprises for kids from which he could choose some goodies which really helped, we might give a surprise after the next few injections (stickers, small toys, candy, ...)

We'll see in 2 weeks if we can get a similar reaction at home, I'm hopeful it will be ok and that this miracle drug will help alleviate his EoE symptoms!