Hi
My LO slept fine as a baby but from roughly from the age of about 10 or 11 months she would have me up 3 of 4 times a night every night. Some nights I would get no sleep at all. Like you I found it was pointless leaving her to cry because she would do it until she was physically sick which left me with bedding to change as well as everything else in the wee small hours. I became an emotional wreck, at my wits end and I absolutely dreaded bedtime. I eventually put a nightlight in her bedroom and it was like someone had waved a magic wand! For the first time in months she actually slept right through and she was fine for quite a while after that. Then she started waking up again. Until then I'd been putting her to bed at about 8pm and it often took up to an hour before she would get to sleep properly. I started putting her to bed at 6pm. She went off within 10 minutes and she slept right through with no problems. I think when she was going to bed at 8pm she was overtired which is why it was taking her so long to get off to sleep. She doesn't have a daytime nap any more so by 6pm she's ready for bed and it also means I get a bit of respite in the evenings too. She does still wake up occasionally but now it's usually because she thinks that 3am is a great time to have a chat!!!
Don't worry about your neighbours. It wouldn't hurt them to show a little more empathy or maybe they just don't realise the situation you're in. They've probably been in the same situation themselves at some time. Is there anyone who could give you a hand, perhaps looking after your baby for a couple of hours during the day while you get some sleep?