The good news is that you're partially correct.
The bad news... Nah, I'll just tell you the solution.
The explanation to your problem is that while the amide C-N or ester C-O bond are single bonds, due to conjugation both bonds show a rather large double bond character (though larger for amides than for esters). This is exemplified by, for instance, DMF, which shows two distinct methyl peaks in proton NMR spectra. Due to the strong double bond character of the C-N bond, both methyl groups are in a different chemical environment (they're either cis or trans to the carbonyl group, and they don't flip fast enough on the NMR timescale). At higher temperatures, these two peaks start to 'melt together' (flipping goes faster) until, at high enough temperature, only one peak is shown.
So, conjugation gives the O and N atoms a preferred sp
2 hybridization, but they also show some sp
3 character (which allows rotation along the C-N bond). In general work however, you can assume that the bond angles are 120°, as these are the most stable.