Unfortunately there is no way to e-file your tax return. The IRS will not accept the e-file without a parent's Social Security number.
Why can't you file by mail? It might be inconvenient, slow, and cost a few dollars, but surely there is mail service to the United States from whatever country you are in.
If it helps, you can get a 6-month extension, until October 15, of time to file your tax return. If you have a payment due, you still have to pay the tax by April 15. You can file the extension online and pay online even if you are filing by mail.
(There is an automatic 2-month extension, to June 15, if you are living and working (or studying?) outside the U.S. on April 15, but it's not clear to me that you would qualify for that. It sounds like you are visiting or traveling, not living abroad.)
