I have a problem with Photoshop layers.

I'll look at it tomorrow.
Is your drawing good in black and white? Why do you talk about putting orange over brown?
In normal blending mode, the color does not change, it overlaps with the other,
In multiply mode, it indeed gives that, I don't get it for now.

Okay, I get it, you only missed one important thing, your "background" layer should have no color.
You paint directly under a colored layer set to multiply mode and not under a new blank layer.
For example: a colored background layer, if I set it to multiply, and create a layer underneath and paint, my colors will darken since multiply mode darkens.
So if I paint brown over an orange selection, my orange will darken.
For example:
http://www.cijoint.fr/cjlink.php?file=cj201004/cijEbNUG9o.jpg
I have the same result as you with the same colors.

To achieve what you want, start with your drawing layer with a white background and black lines, don’t touch it
set it to multiply
create a blank layer underneath set to normal
paint on your new transparent layer in orange, then in brown

which will give you the same result as this example:

http://www.cijoint.fr/cjlink.php?file=cj201004/cijl48Jg1P.jpg
carefully observe the layers palette and zoom in, in the second one I paint in brown on my blank layer colored in orange, in the first one under my background layer colored in orange

since you have already made good progress:
reopen your original drawing (black and white) if you saved it
copy and paste it onto your current file (ctrl A, ctrl C, ctrl V)
Bring your original drawing above and set it to multiply
and set your current "line" layer to normal
Now you can paint on your blank layer underneath without any problem without having to start over.

It's logical, by undoing, you not only repainted but also reapplied certain layers over it without seeing it.
You're not obligated to do everything at once; by saving as a PSD, it preserves your layers and your undo history.

If you no longer have your original file (you should always duplicate and close your starting layer, proof once again ;-)

try this (I don't really know where you are with your colors but it will take you 3 minutes.
You can refine it a bit afterward.

- flatten your image
- duplicate your layer
- go to Image > Adjustments > Replace Color
take the eyedropper tool in the top left, click on each color to remove and slide both bottom sliders all the way to the right
then click OK
repeat for each color except for black, of course, which will not change (otherwise your drawing lines will be erased)

your drawing will only have black and white.

You will then have a layer that you set to multiply mode, and you will have your duplicated colored drawing below, in normal mode (unlock it)
you create a blank layer below it and you can continue without having to redo everything.

Well, thank you very much, Passé simple! Thank you so much! I will try all of this, and if I have a problem, I will post again here =) Have a great day, and thanks again for everything!