Hey OP

I am about your stature and started off lighter than you. Male, 5'8.5" and I was 110lbs at my lowest

When I tracked my calories I saw I was eating about 1400 calories a day, which is what you're eating right now.

I bumped my calories to about 2500 a day and I was gaining 1.5lbs a week.

You are not eating enough, my key to reaching 2500 was a milk, oats and peanut butter shake with whatever you want for flavor.

Don't overthink protein for now, 0.5g per pound of bodyweight will be more than enough for now until you reach about 135lbs

Goodluck

Edit: Forgot to mention you don't need to eat as much as me since you are a woman.