This is only my opinion, I had my tonsils removed when I was 11, it's a pretty straight forward procedure, and the you usually can eat solid food again by the 3rd week. If I were you I would try to move up my 2nd opinion visit, and if they don't have any openings- do what I do and call every day, people always cancel last minute. Or if you'd rather see the doctor you went to last try to get an appointment there. I wouldn't think he'd want to take your tonsils out asap seeing as your nose is still healing. So you probably won't have to worry about being in the surgery setting right away.
About the iv experience, I don't know if they were trying to put it in your forearm or in your hand, personally, when they try to get a vein in my forearm I have the same experience you had and they either blow it or finally get it after what feels like forever .. If it
was your forearm ask them if they'll try your hand first, it's alot less painfull in my opinion and I think it's more convenient. I hope any of this helps, and thanks for replying to my question. :)