Big hugs. You do sound totally exhausted.
First. Is there anyone at all other than your DH who can step in and give you a hand?
I was on my own for DS's first year. I didn't have a single lay in until he was 19 months and I honestly know there are times you reach the end of what can be managed in terms of sleep deprivation. When I was absolutely at the breaking point I asked my mum for help (she was very little help even then, I really needed to be desperate) and I would get her to do the A time, the fun part of holding and cooing whilst I rested or tried to sleep or stepped out the door for a breath of fresh air. Then I took over again for nap time which was the hard part.
Is there anyone at all you can call in just for one or two days to help with one or two A times so you can nap?
Second. Has it been decided that reflux and allergies are all under control? Have you had meds checked for the right dosage etc?
My boy back arched and screamed his head off when he had reflux pain. However he could also back arch when he was UT as he was trying to show me he was not ready for a nap (so wouldn't snuggle into me for his wind down) and just to add to the mix he also back arched when he was ready for me to lay him down (if I didn't lay him down soon enough he would end up crying and back arching of course with him crying I thought I had to hold him but I learned that putting him down he could almost instantly stop crying with a little adapted shush/pat because he wanted his bed). Back arching in my mind can mean a few different things. Do you get a gut feeling or notice any slight difference in the back arching and crying perhaps? Maybe being aware next time you might notice something.
If she is in pain there is no amount of sleep training which is going to stop her being in pain. You do need to be pretty sure the reflux/allergy/teething is controlled or medicated first.
Third. (and only if the point above is a 'yes') It seems to me the gentle increase of A times is not helping you (partly because she is not sleeping much, partly because it is like a long term sleep deprivation for you). Tracy increased A times far more rapidly than we tend to suggest here on the forums. For some LOs small increases are fine, even preferable. However, in your case it may be more productive to go for more of an 'all in' method. Grit your teeth and get a routine in place. Very hard for a few days and absolutely must be consistent but could have more rapid results for you. In the book Tracy begins a new routine with a LO by starting with the set times of when the nap should be, LO is kept awake by any means possible for that A time (Tracy said do a fan dance if necessary) then they are put to bed and helped to sleep (adapted shush/pat in your case). Regardless of how long it takes LO to get to sleep they are woken when the nap is timed to be over to begin their next A time - even if LO took so long to get to sleep that they have only slept 30 mins. They are got up and kept awake for the full next A time until the next nap is due. This may not be easy but I think that's where the fan dance comes in. When it is time for the next nap they are again put to bed and helped to sleep. If LO wakes before the nap is due to end you stay to resettle for 45 mins, if LO doesn't fall back to sleep you get her up and feed her (which may be a bit early). If LO falls asleep towards the end of the nap time you still wake her at the end of nap time to begin A time. It sounds harsh. It is certainly hard work. But it could be just the ticket for you./ What do you think?
If you choose to go forward on this you would need absolute consistency for several days. The idea is that you are not just 'helping' LO to sleep by soothing but you are 'teaching' her, 'telling' her that it is time to sleep. I would suggest a 4hr first A time with the other A times being a bit shorter.
Here is an example, this is not a set-in-stone routine but more of a starting point for working out a routine if you choose to go ahead. I'd welcome pps to comment on the suitability or changes which could be made to this sample routine before it's implemented and if they suggest a long nap with CN or two long naps with a later BT.
7 WU
A 4hr
S 11 - 12.30
A 3.5
S 4 - 4.40 CN (or 4-5.30 full nap)
A 3
BT 7.40 if there was a CN (or 8.30 if there was a full second nap)
Finally. It is important to keep reminding yourself this will not be for ever. you will get through this no matter who tired you feel now, this is just a phase.
hugs