What will happen if I get a second concussion shortly after the first?

Depends. It is difficult to answer this type of questions without knowing the type, severity and the extent of the trauma. And the present symptomatology. The number of events is not necessarily relevant !
Prolong symptoms. A second shortly after a first concussion may result iin a prolonged duration of symptoms. If this is due to a sports injury, do not participate in contact sports until you are completely symptom free. there is concern about a "second impact syndrome", when a brain is recovering from a concussion, somewhat swollen, experiencing another concussion with disasterous results.