Probably a good idea to give up on the blond for now-- you've put your hair through a lot already.  Trying to bleach out all the leftover red would probably fry it.  You should probably take your own advice and go to a salon to ask a professional, if you plan to try anything else with it, especially further blonding.

You should see a professional and get a color correction.

the problem is that if you don't want brassy blonde hair you have to bleach to either yellow or pale yellow depending on how light you want your hair to be. Bleaching to pale orange won't do :P

If you don't dare to bleach the hair allover again. You should let your current toner fade, and then tone the hair again with a blue base blonde level 8 toner.

But you should really consider bleaching the hair again. Most hair can take 2 bleachings without breaking, but if you feel like your hair is in terrible condition the don't. And remember to go slow, obviously highlift wasn't strong enough and it won't work if you try it again, since highlift can't remove even more pigments than it already has. A good bleach is Wella wellite creamlite (use with 20 volume) or Clairol Born Blonde liquid lightener with 2 or 3 activator packettes and 20 volume developer. After bleaching to pale yellow, you'll need to tone. Clairol Born Blonde toners are great and doesn't damage your hair. You can get all these products online or at a beauty supply.