In the US, testosterone is a controlled drug. That means that it is in the same category as Valium, Xanax, and Codeine products. This is because many years ago athletes who wanted a performance enhancing boost would inject testosterone from non-medical sources. The real problem came when the jocks went into "Roid Rage" and their behavior got them into trouble with the law.
It is absolutely mandatory that your vial of testosterone have the pharmacy label with your name, your doctors name and the name of the drug on the bottle. Sometimes a small vial can be placed in a larger prescription bottle, but the pharmacy label must be on the exterior container. A doctors note may help, but the absolute requirement is that the bottle must be properly labeled by a pharmacy.
I cannot repeat this too many times. Controlled drugs in the US must be properly labeled and if your medication is injectable, syringes and prep pads should be in their sterile package unopened. You should only carry enough syringes to administer the amount of testosterone you are bringing with you.