Hi. I had VAT lobectomy 2019 and a VAT wedge resection in 2021. I think your Segmentectomy takes more lung than wedge resection but less than a whole lobe.
Anyway, my lobectomy was overall a bit more painful. For both surgeries, the first day I was up and walking but very painful. Pain was less each day but then around day five, six, and seven it was worse and then improved gradually for the next many months. I was taking the max of Oxycodein, ibuprofen, and acetaminophen for the first few days and off the oxy in a week or so and off all pain meds in two weeks. Was back to most normal activities in 6 to 8 weeks. I still have a tiny bit of discomfort when taking a deep breath and some chest wall nerves are still tingly. Walk and exercise as much as your doctor allows and are able. I was too inactive for too long and had shortness of breath. In my opinion this had more to do with me being out of shape, than loss of lung function.
I hope this goes well for you and they can prescribe agreeable pain medications.
Good luck.