Color management is a complicated subject. (I'm not an expert).
Presumably you printed from a PDF (the High Quality PDF is the best Adobe preset for desktop printers).
It sounds as if you converted your images to CMYK for your inkjet. That's the wrong - you should normally print from RGB.
Once you have converted to CMYK you have a limited color range. You can't recover this by converting back to RGB. You need to start again with your original RGB images.
What are your setting in the Indesign print dialog box under Color Management. Try switching to Let Postscript Printer Determine Colors and see if that makes a difference.
Your monitor may be too bright. Have you calibrated it at all?