Can a person pain from having an arm lift?

Surgery carries risk. Yes, an arm lift (brachialplasty) is a relatively painful surgery. Initial pain is during the first 48-72 hours requiring narcotics but this usually wanes after this period. However persistent pain is a potential risk.
Yes. Yes, any surgical procedure carries the risk of temporary postoperative pain. All surgical procedures also carry a small risk of chronic longstanding pain. An arm lift also carries the risk of infection , bleeding, blood clot, nerve damage, permanent numbness, and anesthetic reaction. You need to weigh the risks and the benefits and discuss them with your physician before deciding to proceed.
Yes. Yes, temporary discomfort after arm lifting surgery is the norm. Longer-term discomfort is unusual but can occur. If this does occur, careful physical examination would be necessary to evaluate the cause and determine treatment for the pain syndrome. Best wishes.