My prayers are with you, too.
I haven't dealt with this for one of my children, but I did find a small non-fixed lump on my collarbone after nursing my daughter one night. So, I completely understand the fear.
Here are a few suggestions based upon my own experience:
1. See what you can find out about your brother's anesthesia allergy and be very proactive in bringing it up well in advance of surgery. You should have an opportunity to speak with the anesthesiologist before the procedure.
2. STAY OFF THE INTERNET - as much good information as there is out there, the desire to know what's going on will take you down some really bad paths and create much anxiety and worry.
3. The hardest part of getting IV is them putting it in - once it's there, it's not bad, and I can't imagine your daughter will be too panicked if she sees it. Just ask them NOT to put it on the top of her hand. It hurts the most there, but the forearm (if her veins are good) has fewer nerve endings and isn't as painful.
4. Don't beat yourself up about it. It sounds like you've been diligent in trying to get answers, and you're being very diligent right now in finding out what's going on.
5. If it is something undesireable, get second/third opinions.
In my case, I had Hodgkins lymphoma (cancer of the lymphatic system) - so, that's how I know so much about IVs, where they hurt, etc. Because of one of my chemo meds, I have to be VERY careful when receiving anesthesia for the rest of my life. The internet led me to my diagnosis before the pathology report came back - that was very scary. I also sought 2 other expert opinions during my treatment and ended-up choosing not to go with my Oncologist's recommendation for completion of treatment based upon the other's recommendations. I've been clean of cancer for the past 15 months and try every day to impress upon other people to follow their instincts and be your own health advocate.
I hope this stressful time will quickly end for your family with the best possible outcome.