Mind elaborating ? If you should be for free trade, should you also not be fro free exchange of labor ?
If you're working in another country, you're not spending money on tax, rent, food, utilities, etc. in your home country, you're spending them in the host country. Most of your income is spent in the host country. For your own example, most H1Bs want to live and spend their money in the US, not send money back home.
So it's actually a terrible 'trade' for the originating country, they lose skilled workers to the US, workers they paid to train and educate, for nothing in return.
What's the 'trade' you talk of? Labor is not trade because what does the home country get out of it?
Free trade is a completely different kettle of fish to free labor markets.
Do you also know that many hotels in the USA are acquired by the Tata Group? The Ritz-Carlton Hotel, Boston is one good example. Again, the group employs only locals and has it's profits stored in the foreign country (US in this case).
There is no reason to believe that trade of goods or capital is lopsided to only harm the United States.