My hair colour is uneven.. Need advice on what to do next!

Firstly, was your hair Virgin or have you previously dyed it before? If it was previously dyed you should have used colour removers first. For future reference.
Secondly, I wouldn't use a high lift blonde, you'd of got a much better result with a bleach & peroxide depending on the darkness of your hair ect. Also you should of waited at least a month before using a highlift/bleach. In future covering your hair in coconut oil a few hours before & bleaching over the coconut oil also helps to not damage your hair as much, many people here do this & recommend it.
If you're wanting to dye it again stay well away from anything with peroxide in it as by the sounds of it you've pushed your hair a little too far, I suggest using a semi. I can't comment on any of the natrual colours as I've never used them myself but I'm sure someone will comment & help with that.
Now I'd suggest for you to baby your hair for awhile, try to avoid using too much heat or no heat at all would be best, use something deep conditioning. A lot of people on here recommend K-PAK.

You have over-processed your hair unfortunately. When you bleach to white, that is generally a step too far. (And yes, hi-lift dyes are bleach, really strong bleach)
I would avoid any further chemical processing or you will have hair the texture of cotton wool hair and/or a lot of breakage.
So no dyes that contain peroxide.
You will need to baby your hair, as you will see more damage over the coming weeks. So minimal washing and styling, protein treatments and deep conditioning. Get a trim, as the damage will travel up the hair shaft, so cut off as much as you can bear to lose.
You can use direct dyes to even up the colour, but you will probably find it has a hard time sticking to the white over-processed parts.
If you add a pic of your current color it will be easier to advise on what colours will match the dark parts of your hair.

Ahh sorry should've added more detail! My hair was previously dyed to a dark brown. Instead of using a color stripper, I used the vitamin c method and got it to a light/medium gingery brown before using the high lift. I waited probably about 3 weeks in between each process, and used deep conditioning, coconut oil, and protein treatments also. It wasn't necessarily bleached to white, more a pale yellow. The purple toner shampoo I used after the second high lift made it white. It definately is still over processed though 🙁

Do all permanent hair dyes have peroxide in them? I know I should probably use a semi but I feel like the white parts won't hold that at all. Thanks for replying guys!

Yes, the developer used with permanent/demi permanent dyes is peroxide. Because these types of dye work by lifting then adding the colour it is less likely to stick to damaged hair than a true semi/direct dye. You don't need any further lift, just to deposit colour and a direct dye will do that without any further damage.

Do not use any more permanent dyes. try the direct dyes if you want to color over it. I know that damaged hair can sometimes be a pain to keep redying as they let go of the color so easily but its better for your hair in the long run. I know from experience.
you can also add direct dyes to conditioner so you can condition and dye at the same time.