Obtaining a Thai driver's license is possible with a tourist visa, and you can do it with or without an agent, even in rural provinces. To apply, you'll need to provide proof of residence and, if you have one, your old driver's license from your home country. If you don't have the old license, that's okay - you can still apply. The process is simple: you'll take a written test and then proceed to the driving ground for a practical assessment. The staff is very helpful, making the process easy and stress-free.
Try contacting the call center, they may not know much about visa issues. If you're not successful, you could try visiting the bank and explaining your situation, including the new iPhone. Sometimes they can be helpful.
Sorry to take over your comment, but my school in Thailand is putting together the paperwork I need to apply for a visa. I have a three-year university diploma as well as a postgraduate diploma (level 8, just above a degree), but I'm not sure if they will accept it since many people say you need a degree and I'm in the middle of my Masters in philosophy, which is due to end next year. I have saqa verification in addition to having studied in South Africa and being a South African, so I'm unsure if this is the right course of action.