import aiohttp

WORKERS_COUNT = 5
df = None


async download(session, url):
    async with session.get(url) as response:
        assert response.status == 200
        response_text = await response.read()

        return {
            'status_code': response.status_code,
            ...
        }


async process_data(row_index. session):
    url = df.loc[index, 'url']
    data = await download(session, url)

    df.loc[index, 'status_code'] = data.get('status_code')
    ...


async def worker(q, session):
    while True:
        row_index = await q.get()
        # todo: остановиться если очередь пустая
        await process_data(row_index)


async def main(loop):
    global df

    df = pd.read_pickle('with_sent.pkl')
    # инициализировать данные
    ...

    q = asyncio.Queue()
    for i, _ in df.iterrows():
        await q.put(i)

    with aiohttp.ClientSession(loop=loop) as session:
        tasks = [
            loop.create_task(worker(q, session))
            for _ in range(WORKERS_COUNT)
        ]

    await asyncio.wait(tasks)

    # сохранить данные
    df.to_pickle('output.pkl')