Bulging vein on cheekbone is treatable
If it is indeed bulging as you describe, ultacision microphlebectomy would be a rather straightforward treatment. I combine it with sclerotherapy immediately before excision to minimize bruising. Expect to spend $1500 to $2000 for such treatments on the face. look for a vein specialist or a plastic surgeon who is comfortable dealing with vein problems on the face.
There are several doctors who can treat this vein but a vein specialist or vascular surgeon would be appropriate. Depending on the size of the vein and its location, there are several options for treatment including sclerotherapy, laser or microphlebectomy.
Blue Vein on Cheek
It is difficult to assess your blue cheek vein without a photo but it sounds as though this would respond to laser treatment. Fat transfer does not address veins so I would not have expected improvement of the vein following this procedure. I would recommend consultation with a board certified physician experienced in using the 1064nm laser for vascular treatments. Best wishes.