Moms can be pretty protective.
You can't go through your life expecting your mom to approve of everything you do and who you date. In her mind she already has some sort of plans for what she wants for her son.
My advice here is to feel out what your mom dislikes about this girl (and do others dislike the same things...cause your view of her is bias cause you are into her already) and maybe try to overcome these things with some positives.
4 months isn't a longtime so it will probably take more time....patience will be key here. your mom may be playin tuff in the beginning and who knows she may open up, relax and everything will work out fine.
Or you could make a stand and push back on this with your mom...although I wouldn't advise it moms usually don't react very well to this approach.
Good luck!