The title pretty much says it all. If I file a patent in the US, will forign companies be able to use it without fear?
Most likely, yes. You may have some options if the competitor's product is imported or if the invention is a process used to make a product that finds its way to the US.
Patents are specific to the country in which they are issued.
Technically it is not the company being foreign that is the issue, it is where the activity occurs. So IBM can make your US patented thing in the UK and sell it in China - if we are talking about a patented thing.