C++ Write a program that prompts the user to enter a person's date of birth in numeric form (Throw/Catch)

I have written a code already, and it's a little tricky. I'm trying to get it to where the user writes their date of birth (ex: 12/05/1990) and it outputs their birth as ("December 5, 1990). I have already written the else/ifs for invalid Months and invalid Days. I'm for some reason not being able to get the day and year to display. For example; it's only displaying correctly the month which is "December" and I'm getting a bunch of numbers for both Day and Year which are completely wrong. Also, any ideas of I should do for the program to be able to handle LEAP YEARS, for every 4 years. Any help is appreciated. thanks!

#include <iostream>
#include <string>

using namespace std;

struct invalidDay : public exception 
{
const char * what() const throw () 
{
    return "Invalid date, try again.";
}
};

struct invalidMonth : public exception 
{
const char * what() const throw () 
{
    return "Invalid month, try again.";
}
};

int main()
{
int day;
int month;
int year;
string monthName;

try 
{
    cout << "Enter birthday: mm/dd/yyyy : ";
    cin >>month>>day>>year;

    if (day > 31)
        throw invalidDay();

    if (month == 1) {
        monthName = "January";
        if (day > 31)
            throw invalidDay();
    }
    else if (month == 2) {
        monthName = "February";
        if (day > 28)
            throw invalidDay();
    }
    else if (month == 3) {
        monthName = "March";
        if (day > 31)
            throw invalidDay();
    }
    else if (month == 4) {
        monthName = "April";
        if (day > 30)
            throw invalidDay();
    }
    else if (month == 5) {
        monthName = "May";
        if (day > 31)
            throw invalidDay();
    }
    else if (month == 6) {
        monthName = "June";
        if (day > 30)
            throw invalidDay();
    }
    else if (month == 7) {
        monthName = "July";
        if (day > 31)
            throw invalidDay();
    }
    else if (month == 8) {
        monthName = "August";
        if (day > 31)
            throw invalidDay();
    }
    else if (month == 9) {
        monthName = "September";
        if (day > 30)
            throw invalidDay();
    }
    else if (month == 10) {
        monthName = "October";
        if (day > 31)
            throw invalidDay();
    }
    else if (month == 11) {
        monthName = "Noveber";
        if (day > 30)
            throw invalidDay();
    }
    else if (month == 12) {
        monthName = "December";
        if (day > 31)
            throw invalidDay();
    }
    else if (month > 12)
        throw invalidMonth();

    cout << monthName << " " << day << "," << year << "." << endl;


}

catch (invalidDay& e)
{
    cout << e.what() << endl;
}
catch (invalidMonth& e)
{
    cout << e.what() << endl;
}

system("pause");
return 0;



}