Welcome to Healing Well! While I didn't have the TIF, I had the hernia repair and Nissen Fundoplication surgery.
From what I've learned, it seems that the shoulder pain comes from two sources--loose gas in your abdominal cavity (the doc blew you up with CO2 to create an easier viewing field) and irritation to the diaphram.
In my experience, walking helped reduce the shoulder pain. If you can get up and start walking around your house, and when weather permits, outside. No guarantees, but I found that the more I walked, the less my shoulder hurt (and visa-versa).
The esophagus is a "dumb organ" and it interprets all pain as "heartburn". It's more likely that the pain you're having that feels like heartburn is really generalized pain from the surgery. Your increased pain is likely caused by increased swelling putting pressure on the device and your esophagus. Be sure to call your surgeon whenever your pain seems extreme, so he/she can speak to its cause. I'm sharing my own experience, and am not a doctor.
My guess is your headache is a result of the anesthesia. A good friend of mine always gets headaches and nausea when she has surgery. She now informs her anesthesiologist, so he can adjust the medication accordingly. That's why they always ask if you've had any trouble with anesthesia before.
Swallowing will be pretty dicey for a while. Just take tiny bites and eat and drink very small amounts at a time throughout the day. Things will get better. It just takes time.
Try to be patient. Hang in there. Things will get better!