I was in pretty much the same place as you. Diagnosed as a T2 in 2007, went all the way through the oral meds, and in 2019 with my HbA1C above 100, My doc advised me the same. I resisted for about 3 weeks, but got nowhere with dietary changes. Going on insulin was a liberation. My HbA1C dropped to about 55, and the injections whilst a bind are a small price to pay to stay healthy. Insulin is stored at room temperature once started, and will last a month. To be honest, I would expect your insulin dose to be very low initially (below 10 units per day), and the pens are 300 units each, so will last a good while. I have a cool bag for carrying mine when I go to the Med, but in reality, it's not the problem people make it out to be if just going for a couple of weeks. It's prohibitively expensive in the states unless on a health plan, so I'd not be a fan of buying any there. I just took a couple of spare pens of slow acting when I went to Boston in 2019 for 10 days, and brought them back with me as I was only on about 8u then.
I'm now on 32U of basal, and carb count for the bolus at 1u per 10g of carbs if I get a spike after eating (10g of carbs is a digestive biscuit)