Check oil light on

Welcome to 2CarPros. From your description it sounds like there might be an internal engine problem causing either oil burning or loss depending on how far you have driven it in those three months. Could you take a picture or video showing the engine oil and check the oil level on the dip stick? You may have a low oil level and driving it with the light on will likely do more damage. As a start check the oil level with the car setting on a level spot. If the oil looks dirty and black or worse looks like a chocolate milk shake then there is a problem.

That looks like you are getting coolant into the engine likely through a failed gasket.
At the moment I would probably flush it, then track down the leak and repair it or swap the engine out.
The second option would be better if the cars oil was like it is now the first time, that would be because you don't know how long the other owner drove it this way and coolant does bad things to the bearings and cam surfaces it gets on.
It doesn't sound that bad in the video but you never know how bad things really are until you open the engine up and inspect it.
You could find a good used engine, replace anything that is due for work and then install it, probably for less money than rebuilding the one you have.