It's difficult to give an answer or guidence to your question without knowing of the medical history or any medications taken. There are certain medications that can cause side-effects that cause dizziness. Many heart patients take coreg (beta blocker) and lisinopril (ace inhibitor) that may cause dizziness from low blood pressure, or just as side effects.
Has blood pressure been pressure measured when your grandma is standing up for three minutes? If the standing blood pressure is below 90, that's the cause of the dizziness, and maybe less lisinopril will avoid the dizziness. IF the blood pressure is above 90 when standing and still dizzy, report the dizziness to the doctor.
Dizziness is not one of the expected side effects and not included with know symptoms:
Loss of appetite
Swelling in the area from which the segment of blood vessel was removed
Difficulty sleeping
Constipation
Mood swings and feelings of depression
Muscle pain or tightness in the shoulders and upper back
Mild disorientation
Some temporary memory loss
Poor concentration
Fatigue
Many of these side effects usually disappear over the course of four to six weeks, although a full recovery may take a few months or more.
10 fast breaths taken in will make a healthy person dizzy; it's called hyperventilating. You are actually getting less oxygen. It can take months for the body to repair itself after the onslaught of a major surgery so what this person is going through, as well as yourself, is probably not a problem at all. After having a surgery, you would find that your brain function would probably improve because of better bloodflow.
I wonder if there is more to it than that. I remember having light headedness for about six weeks after a triple bypass. I also had the exact same thing when my LAD was opened with 5 stents. I cant help but wonder if the body simply becomes more efficient at transferring oxygen and you have to wait for the body to adjust again. Before I had my stents, I could breathe very fast and never reach a point of becoming light headed. Now after about 10 fast breaths, I'm spinning. Is it possible it's just more oxygen available and it takes time to get used to it again?
Another similarity is when people go to high altitudes. Over a period of weeks their body adapts to the lower oxygen.
2nd, 3rd, and 4th day you should still have been in the hospital and should have asked about it there. Grendslori is right but there is also the medication, anesthesia, and probably a slew of other things. Unfortunately I had overdosing problems so I can't give a good review in this regard but I will say I felt very week for the first couple weeks.
It has a lot to do with the fact you are spending the majority of your time inactive while trying to recover. A person can have abdominal surgery and face the saame problem. Your body has to get used to being up and around again in it's normal fashion. Hope you are feeling better real soon. you should be.