I'm sorry I didn't say this first. If you're having doubts, it's ok to just go and find another doctor. Your comfort level and your health is what's most important. You need to feel good about going to the doctor and taking your kids to the doctor. If you don't feel good about it, change doctors. That's reason enough.
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I know it's not possible for you to include every detail, so please forgive me if you've already done these things and just didn't mention them.
I think it's quite possible that my 5 year old has Autism. Our pediatrician told us she not qualified to make that diagnosis. He was seen by a behavioral, pediatric psychologist who did not believe he met the criteria for Autism. One of his therapists disagrees. We are going to see a developmental pediatrician to see if we can't get a definitive answer.
I don't think a general practitioner is at all qualified to make that determination. I'm sorry that she challenged another professional's diagnosis. Did she give you a reason? That would frustrate me for sure!
As far as the other two concerns go, based on teh information you gave I think you definitely could have been more proactive (maybe you were and you just didn't mention it).
Iron supplements can be purchased over the counter, which is probably why your insurance refused to pay. I've had that happen several times, and the only reason the insurance company gave was that it was available OTC. If she needed to call it in, she probably wanted you on a very high dose. When your insurance refused to pay, did you notify your doctor and ask what you should do? (Because it sounded like you just expected her to know that your insurance refused to pay, and I don't think that's something she would know unless you told her.) All you really needed to do was clarify with the pharmacist the dosage she wanted you on and how to do that using the OTC iron supplement.
When you were waiting with your child for the routine check-up, did you check back at the receptionist's desk 15 minutes after your scheduled appointment time and then again 15 minutes later? At our doctors' offices there are signs saying to let them know if you are still waiting 15 minutes after your scheduled appointment. I have to admit, our doctors are usually very, very good about staying on schedule. But they are only human, and sometimes Nurse Suzy things Nurse Kim is taking care of you and Nurse Kim things Nurse Suzy is taking care of you, and so you get missed. If you say something right away, they will check and make sure you are the next person in line. I would never wait an hour before letting someone know.
I've been very lucky, because most of the doctors I've had were very, very good. But I'm not at all shy about calling back if I have a question or feel at all like they've missed something. I try to be very nice about everything, but I am persistent.
But I am also very appreciative that my boys have a pediatrician. I've been very pleased with our pediatrician - she has never rushed me and has really listened to my concerns about our 5 year old. She has also been very thorough and has picked up on things that other doctors might have missed.
My husband and I see a general practitioner. We really like him!!! He's great. But he agrees that our boys are better served by a pediatrician. I'm sure he would do a good job, but I'm happy with their doctor as well.
ETA - Just an FYI after reading Leigh's response, my OB had me take iron supplements when I was pregnant with my, now 8 year old. Those I bought OTC. I had sever bleeding when he was born, and she prescribed iron for me then. So it is quite possible for you to be prescribed iron. But just like ibuprofen, it can be prescribed in higher doses.