Sarah, sounds like Braxton Hicks to me, they can feel alarmingly like the real thing but they do go away eventually. Try drinking something as they're worse if you're a bit dehydrated. I'm 36 weeks today too, and have only started having them over the last week really, whereas last pregnancy I'm sure they started much earlier, and my first pregnancy I had none - it really varies.
Lolo - ice craving can be a sign of anaemia I read, I think you posted that your hb was a bit low? Nothing to worry about anyway.
Someone else posted something I was going to comment on....oh yes swigging Gaviscon - my midwife told me that if you really go overboard on it it can show up in the placenta which can be visibly calcified, so she recommended Slippery Elm - I'm not suffering too much from heartburn at the moment so I'm not too bothered but if your heartburn is terrible Gaviscon and similar should be used with a little caution...
Scan weight estimates can be pounds out, so a better guide is whether you feel you're carrying a big baby or not - I don't feel this baby is as big as my last (DD was 8lb) so I'm expecting it'll be 7lb something, we'll see....it's mostly head down and anterior (can feel hiccups very low down so know it's head down) so a change from my last couple of pregnancies where they were breech till late on, although I'm not sure it's not turned in the last day or so, felt hiccups round my bellybutton last night! My midwives have had 2 breech homebirths recently so at least I know they've got some recent experience if it does come to that.
Still don't feel anywhere near ready to have the baby but once the kids are back at school next week I'll do my final bits of preparation, get the birth pool next weekend I think (hiring a heated one with a lockable cover, so I can relax in it in the evenings), and then whenever....DS1 has important exams right around my due date so hopefully it will either be earlier or later than that, don't want to distract him!
I'm sure there was more stuff to comment on but this is long enough so will resist!
Good luck if you have your babies this week Mini