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Both the USA and Canada only require a passport to be valid for the period of intended stay FOR GERMAN CITIZENS.
Normally when entering the USA and Canada you would be granted entrance for 90 days/6 months respectively, however given your passport will expire before that period is up you will only be granted entry until the expiry date on your passport.
In future I would strongly recommend not cutting it this close with the expiry. If something goes wrong whilst you are in the country and you end up having to stay longer than expected it can cause real problems. Some countries also enforce that your passport must be valid for at least 6 months at time of entry, but thankfully neither the US or Canada do that for GERMAN CITIZENS however the US does requite 6 months validity for citizens of many countries.