You've raised several questions.
While getting your green card makes you a US resident for tax purposes, you may have already been a tax resident based on other rules, the "183 day test". This gets complicated so you may need professional help. Tax residents are taxable on their worldwide income, no matter where earned. So you would include the 3k with the rest of your US income when filing your 1040. The foreign tax credit is intended to avoid double taxation, in case there is a Canadian liability.
I do not know if Canada requres you to file, but you should be abe to check this online at the CRA website. There is an income tax treaty between the US and Canada that may impact your situation. This is available online at the IRS site.
From a common sense perspective though, I doubt if there is 3.5k of Canadian tax on 3k of income. The same for CT.
