Generally, milk paint is like any other lime-based paint, and is very matte. One way to figure out what kind of paint it is is to try different thinners/removers on it. If you wet a sanding sponge with water, then alcohol, then mineral spirits, and then trying it on the paint with each separate fluid, which one pulls up color and paint will tell you more about the identity of the paint. You probably should also try one of those lead-check tests first to see if the paint has lead in it. That data will inform whether you should be sanding much at all.
The best way to determine what paint it is to rub an area of the paint with alcohol or even a paint deglosser.Here are some tips to paint over a pre painted wall:
First of all wash the wall to remove any of the grease present then fill the holes and cracks with a filler
Sand the filled areas and then prime it the priming would seal the filler and keep it in place.You could even sand and reprime the wall
Always repaint the walls with at least 2 coats of paint.If you are painting a light color over a darker one then you might want to have more than 2 coats to keep the color from showing
It is always better to paint in full daylight as you can see properly what you are doing.
You might even want to hire a residential cleaning service to help you clean the house while you are renovating.I had the services of rbc clean when I was having my house renovated.Here is a blog that mentions the benefits of hiring an insured cleaning company
Milk paint is definitely not thick and shiny. More likely you have lead paint. I would clean the walls with TSP (Tri-sodium Phosphate) in a warm solution. Allow it dry thoroughly and seal the surface with either Bin (pigmented Shellac) or Kilz.
This will provide you a solid substrate on which you can apply any paint. Bin is extremely thin and smelly, but offers the best adhesion. If you are going to use a dark color then tint your seal coat to a dark gray depending on how dark the chosen color is.