I went to the orthodontist and the glue they put caused burning and mouth ulcers. Does this mean I am allergic?

Doubtful. If anything you may be extremely sensitive to the very slightly acidic (like vinegar) material used to help prepare your teeth for braces placement. May also be herpes outbreak caused by the manipulation required to place your braces. Go back to your Dentist or (hopefully) Orthodontic Specialist for reevaluation and treatment to help you feel better.
Something else. Think your symptoms were caused by something other than the adhesive.
NO. There is a gentle acidic solution used to prepare the teeth to receive the dental adhesive. You might have gotten some of this solution on your soft tissues and had some burns as a result.
Most likley not. If you noticed the burning immediately after the procedure then it might not be the glue. Sometimes the acid based cleaner they use prior to adding the glue can creep onto tissues and cause burning and ulcerations. Your mouth should heal pretty quickly (in a few days), but if the ulcerations do not heal in 1 week, then call our orthodontist.
Possibly. I would go back to the orthodontist for an evaluation. It could get worse so i would call asap.
No. It is probably the etchant which is a mild phosphoric acid gel used to etch the teeth to prepare them for the bonding. The resin "glue" used to bond the braces only adheres to etched teeth. If it gets on the soft tissues, it can cause a slight "burn". It will heal.
Probably not. I suspect that the tooth conditioner (citric acid usually) got onto you tissue and caused the irritation. Sometimes we see a primary herpes simplex breakout due to the combination of factors of the lip retractors, citric acid and placing of the braces. The microtrauma of these combined can get a primary event started, if the patient hasn't had one already(they usually occur during infancy).