Typescript 'Cannot find module' with declaration file

I'm using typescript with react and need to provide typings for a third party library called react-sticky. I don't want to publish a typings module, I just want to write the typings and include them in my codebase, but I'm running into trouble. Here's the setup

App.tsx

/// <reference path="./typings/index.d.ts" />/// <reference path="./typings/react-sticky.d.ts" />import * as React from "react"import { Sticky, StickyContainer } from "react-sticky"const App: React.StatelessComponent<{}> = () => {    return <StickyContainer><Sticky><h1>Hello World</h1></Sticky></StickyContainer>}

/typings/react-sticky.d.ts

/// <reference path="./modules/react/index.d.ts" />import * as React from "react"declare module "react-sticky" {    export var StickyContainer: React.Component<{}, {}>    export interface StickyProps {        stickyStyle?: any        stickyClassName?: string        topOffset?: number        bottomOffset?: number        className?: string        style?: {}        onStickyStateChange?: () => void        isActive?: boolean    }    export var Sticky: React.Component<StickyProps, {}>}

typings/index.d.ts

/// <reference path="modules/react-dom/index.d.ts" />/// <reference path="modules/react/index.d.ts" />/// <reference path="react-sticky.d.ts" />

The error I'm getting is the following

App.tsx(3,41): error TS2307: Cannot find module 'react-sticky'.

Now, I'm new to Typescript, there are quite possibly multiple errors here, anyone know what I need to do?