Dyeing to blue, purple or green from dark brown and scared to bleach :P

Hi all!
Before I start: I'm not a punk, nor do I like heavy metal or rock music. I'm more into europop and classical than anything else. 😉 But I have wanted hair in crazy colors for, like, forever. 😛
My hair is very thick, medium-dark brown and wavy. A couple days ago I finally got my mom to let me dye a small bunch of strands behind my ear, so I went to a small hair salon and had it done dark blue and then straightened. It looked near perfect, except maybe a little dry, until I showered--even though I used tons of conditioner, it now looks very dry and frizzy! I've wanted soooooo badly to do ALL my hair for years, and this is my first ever time dyeing it...now I'm scared all the rest of my hair will turn out like this! Before, it was really hard for me to get my hair to stay straight...now I burned out pretty much the only curl on my head I really liked  *ott*
Basically I want the top (or part?) of my hair to be light blue, like in this picture:

And the bottom to be either the same as in the aforementioned picture, or the green or purple shown below:

All the conflicting information on the Web and advice from friends and family is confusing me! I'm determined to dye my hair unless it should prove impossible to do it and not have it look frizzy and ugly. Also, I'm in Mexico and my mom will NOT let me bleach and dye it myself, not to mention I'm scared to do it now 😛 Is there any specific type of salon or whatever that I should look for so that I can have dyed and decent-looking hair? I use Organix brand coconut-oil conditioner and Brazilian Keratin Therapy, is that OK? It's all I have :$ Or would I really get better results by doing it myself? I want it to look as soft as it does in these pictures (the green one is an advertisement for a green hair dye, haha 😛 ), and I don't want any wigs! XD
Is there any way I can bleach it myself without so high a risk of damage, so that I can more easily convince my mom, and then go to the hairdresser's to have it dyed my final choice of color, once it's already pale yellow to white? Can this be achieved with bleach baths? And if so, any particular brand of bleach and/or shampoo you'd recommend, that I can actually get a hold of in Mexico?
Please help! This is my first ever time dyeing my hair so I'd really appreciate any pointers 😀
Thanks in advance 😀