Wow, I had practically the same problem with my dd, she was my first so I didn't have a toddler to cope with as well. You have my deepest sympathy, sleep deprivation almost ruined my life.
At 6mo dd started head shaking to keep herself awake, by 9mo she would hit herself in the face, rip out her hair, basically do anything to keep going.
Giving up breast feeding at 18mo made a difference, but she really only started sleeping for more than 6 hours at a time when she was 3. The No Cry Sleep Solution helped allot.
Before this we tried every sleep training method there was including cc. Nothing worked and even the sleep specialist we saw said our dd had greater issues.
Food was also a nightmare. Dd wouldn't eat solids till she was 13 months, we got her to take a cup of warm milk by putting baby Einstein on the tv.
Sorry this all sounds a bit depressing but I just thought I'd give you some background.
When ds was born I felt like he was following the same eating / sleeping pattern so I came on here to ask. The wonderful MN diagnosed him with reflux, I went to the doctor and was prescribed gaviscon. The difference was huge straight away, he slept through really well. At 6 mo I stopped the gaviscon on the doctors advice as he was eating solids really well. By 7mo he was awake all night again, so we went back on the gaviscon. Then at 20mo he started waking and screaming so we got sent to special doctor.
This doctor was a gastric specialist, he put ds on omniprazol which worked perfectly.
While I was there I asked about Dd saying that I think she'd had similar but seemed to be better as she's got older. Doc said that reflux is really common in young babies and kids. It's one of those things that people often think their child is just a bad sleeper and they grow out of it. In reality these kids have reflux and are not able to say its uncomfortable and they want some company.
In my dd's case, she never learned about sleeping properly so she still has to be hugged to sleep and gets up at 6am every day no matter what her bedtime.
So after that massive rant. Basically I recommend getting some baby gaviscon and giving it a go for a week. If it helps then you could try and trace the source of the problem, maybe wheat or dairy sensitive but not intolerant.
Good luck.