Yes, you can recover US federal taxes you paid in error. If in your circumstances you held the J visa as a "teacher or reseacher", the tax treaty does exempts you from income tax for 2 years, on "wage" income, ( per pub 901 Tax Treaties, p52, available on the IRS website,
Internal Revenue Service, type in Pub 901 in the search box).
How do you make this correction?
You make this correction by filing a form the IRS provides for making corrections, Form 1040X. See the instructions for this form, 1040X Instructions, page 3, under "Resident and nonresident aliens". It states the specific instructions you need to follow to make this correction and receive your refund.
(Please note: you'll need to site the specific treaty reference that allows this exclusion, its Article 20A, of the Uk treaty).
Remember, you must file this correcting return to claim any refund generally within 3 years of the original filing, or 2 years of paying the tax, whichever is the latest, or it
will be disallowed.
Good luck on your filing