I suggest: "Yes, I am still seeking employment, and I am willing to relocate to the United States."
The word needs to be "seeking," not "finding." "Seeking" means making a search, it is the process of TRYING to find something. "Finding" means the search is over, the goal has been reached.
It turns out that both U.S. (with periods and NO spaces) and US (without periods) are considered acceptable abbreviations, but U.S. with periods feels better to me. The easy solution, and also the most formal and correct, is not to abbreviate it but just to spell out "United States."