nc - you must be exhausted, sleep deprivation is so hard and can effect your health and your relationship with your baby, so you're right to think about what you can do to try to improve the situation (rather than feeling you have to be a martyr about it).
I'm not going to recommend a particular sleep training method as different approaches work for different babies. Try a few out and see what works best for you.
In the meantime, try to get any help you can, from your partner (if you have one), from family, friends, a paid maternity nurse or sleep consultant if you can afford it.
We went through sleep hell with our dd from around 4-5 mths until 10 mths, then we did cc (with shorter timescales, 2,4,6,8 mins etc). I was due back at work so we couldn't continue taking turns to get up every 1-2 hrs.
If its any comfort dd (now 2.7) is a perfectly normal, confidant, happy, sociable, affectionate toddler. Who sleeps very well.
Can you introduce a different sleep aid? We used a dummy so at least when we got up we only needed to pop the dummy back in (dd dropped her night feeds quite early on herself so wasn't waking for milk).
I do hope this thread will focus on supporting the OP rather than turning into a bun fight...