What we need to fix if we created link using application administrator console which is not shown on DWA( MyIT Admin Categories section)
There is an idea existing for adding Icons to Quick Links. Please vote: Add Icons to Quick Links DWP MyIT 3.5 and earlier
Yes, there is a possibility to achieve this by modifying the myit.css-file. I've done this last year, but it stopped working after a patch/upgrade and therefore I wouldn't recommend that as you always have to do it again after a patch/upgrade.
For further information, check this out: How to add an icon to a Quick Link?