Oh dear, sorry to hear that. Depending on the type of paint that messed on the carpet you can try one of these : https://spotremoval.coit.com/how-to-remove-paint-stains-from-carpet
If commercial solvents don't work I would try to carefully cut tiny pieces of the carpet fibers with bits of paint on them with very sharp scissors to break the paint spots apart and see if you can pull some of the paint bits off by hand....then try rubbing hard to see if the other paint pieces come apart/off. Depending on the pile/weave of the carpet this often works. Good luck!
As a retired building and remodeling contractor. You can be very careful and use Oops, that is one of the best over the counter one and has many other uses as well. Another is Lestoil, be careful with both and don't oversaturate the rug. Both will dissolve or soften the adhesive holding the yarn fibers to the back of the rug. Apply either sparingly working into the fibers with your fingers, it's tedious, but better than replacing. Accidents happen no matter how careful you are.
Alcohol will remove latex paint from anything....even from washed and dried clothing. Apply alcohol and scrub with a clean cloth. Repeat until removed!