I had this problem for years! Burning lady parts, no itch, no infection, no STDs. I found a couple of remedies: baking soda water, Cystex, heated pad on lower back, please read explanation:

I suffered from age 16 to 29. Doctors put me on antibiotics and pushed cranberry juice, cran supplements. I went to an OB, she did a biopsy, for unrelated reasons! Like I cared, I wanted the burning to just stop! I felt like every time I worked, got stressed out, was excited, had sex, and before and after my period, I was plagued with this life destroying vaginal burn. Sometimes it'd me mild and most times it'd be so intolerable all I could do was sit with my head in my hands and endure. I would not wish this on my enemies.

I stumbled upon a thread that had suggested drinking baking soda/sodium bicarbonate mixed with water, about 1/4 tsp to 8oz water ratio. This actually helped, within 10-20mins! However, a year later I developed heart burn problems. 

I was finally recommend a urologist, who diagnosed me with cystitis (IC), (which cranberry anything causes the bladder to flare up bad, invoking more intense vaginal burning) and pumped my poor bladder with sodium bicarbonate, which is baking soda! (That's how they treat it. My urologist wasn't at all surprised that the baking soda water helped) 

But here's my real relief....the urologist suggested I start an over the counter supplement called Cystex. I get it at Walmart or Walgreens or CVS. It's right next to the cranberry supplements. It works for me and it costs me $11 for a box! Here's the twist for me. Cystitis and IBS run hand in hand, and when I'm struggling with IBS the Cystex, though helps a bit, it's not 100%, I have to let my bowels run its stupid course and then all better. 

Another thing that helps me is actually laying on a heated pad on my lower back. Took me years to figure that out, but it helps way more that trying to numb the south parts alone.