You wouldn't be able to count accurately at all. How will you tell what would have happened without treatment? Does giving a vaccine save someone's life? That kid might have caught meningitis and died, or they might not have. You'll never know. And really, was it you saving the life, or was it the researchers that developed and tested the vaccine? The nurse that administered it? The parent that signed the consent form? The PSA that told them to vaccinate?
Most of medicine is not pulling people back from the brink of death. Even in the ER. And you are never working alone. You are working with a huge team. So say you you have a patient with chest pain so you order an EKG and the EKG tech does the test and you interpret it you ask the nurse to draw troponins and the nurse draws the troponins and the lab tech runs the test and the pathologist interprets it and comes back positive and you send to the cath lab and the cath lab doc does a cath and the cath lab techs run the imaging machines and pull out the catheter and the post op nurses recover the patient and their wife stops them from getting out of bed and bleeding out afterward. Who really saved the life there? Even in my simplified scenario you can really only say you saved 1/10 of a life. And who knows whether it will give the patient another 30 years or if they will get hit by a bus tomorrow when they walk out the door, and if you hadn't cathed them they would have left at a different time? No one knows that kind of thing. No point counting, just do your job.
And I worked four years in a hospital, attended daily codes, and never saw a doctor do compressions. It was always nurses or RT's, because they would get there first. So you will probably not be doing much actual literal lifesaving either.
And really I hope you "heal" more than 300 people in your career. That's like ten a year.