If someone has two concussions within two weeks is there a possibility of brain damage?

Yes possibly: There is increasing awareness of brain injuries which are below the level of detectability with current imaging techniques, like ct and mri. The bottom line is that you should be cautious, and you should consult with your doctor if you do not feel "right".

Possibly: Repeated concussions within a short period of time are bad because of the cumulative effect of the concussions. It is well known that the brain is hypermetabolic after a concussion. Thus, it is more sensitive to the effects of additional concussion, particularly if there has not been sufficient recovery time (usually 6 weeks minimum).

Evaluation: There is indeed a concern for cumulative damage, but give it some "brain rest" and tincture of time ~6 WEEKS, and reassess. If there are headaches, visual changes, vomiting, dizziness, cognitive or emotional challenges, seek help from your doctor. Neuropsychological testing or vestibular/ otological studies could objectify lingering problems.