Right now I have a maxed out character with really good gear, but there are many unobtainable things i cannot get because of my stupid mistakes in the past. (i.e: not picking up assassin's armor, killing many NCR quest givers, not getting the Legion Safehouse key when "liked" and then killing Lucius, killing Boone....) Can I start up a new character without losing my old one?

Yes you can - the game will just create new save files for your new character. Depending on how many saves you already have, you may want to go back and delete some of the old ones that you won't use again, to make managing them and switching between characters easier.

Create another profile

That's about the only way to do it safely without having to worry about deleting and or saving over your other saves

Yup, make a permanent save for that character and dont save over it. I got about four different ones going on right now.