This is Lawrence Watt-Evans' Obsidian Chronicles trilogy: Dragon Weather, Dragon Society and Dragon Venom.
The story opens with the MC's family/village killed by a dragon, which drips venom on him while he's hiding from it. He wants vengeance but is surprised to find out at the end of book 1, many years later, that being dripped on by a dragon is how dragons are created, and that he is going to become one.
“Dragons destroyed my home village,” he said. “At least three of them. They came nine years ago, during a long spell of dragon weather. I was in the family cellar, taking inventory to see how much we needed to add before winter, when they attacked. My grandfather was killed by a blast of venom that failed to ignite, and he fell down the cellar ladder onto me as he died; his blood, and the venom, spilled into my mouth as I lay stunned beneath his corpse.”
And yes, eventually he lives in the attic of a brothel.
“Where am I?” he said. “Who are you?” He wanted to ask why she had seduced him, as well,
but couldn’t think of any decent way to phrase it.
“You’re in the House of Carnal Society,” she told
“The what? ” he asked.
She giggled. “It’s a brothel, silly! Hadn’t you
Arlian looked at her in embarrassed confusion.
“What’s a brothel?” he asked.