Start by looking into how to get a work visa for the countries that interest you. Then focus your search on those for which you can get a permit. You may find your unique heritage and cross-cultural strengths helpful in opening doors. Consult "Hoover's Handbook of World Business" (Hoover's Inc., 2001) to target larger companies that do business in or plan to expand into your home country. Other resources include your university career center and alumni who work in these countries already.
Dwelling on your need for health-insurance benefits may cause problems. It isn't good policy to hide important facts that affect your job performance from would-be employers, but it also isn't smart to open discussions with your health issues. You'll need to find a middle ground.
One approach is to seek a short-term contract for which insurance issues likely wouldn't be brought up initially, since you wouldn't be considered a full-time permanent employee. After you've proven yourself, you could approach a manager you trust to discuss the possibility of your joining as a full-time employee with full insurance benefits. You then could briefly explain your improving health situation.
You may be able to pay the premiums for your existing insurance during a transition period. This would allow the time you need to get started in your career.