If statement does not work in Switch case

This may help:

I can see why you want to use the switch-case structure, as you have lots of different modes.

I'd recommend you break your code up into functional modules, eg

void countPushup()
{
    a ++; //print a point if a pushup has been done
    Serial.println(a);
    BT.println("Push-Up");
    BT.println("Counts:");
    BT.println(a);
    lcd.clear();
    lcd.setCursor(3,0);
    lcd.print("Push-Up");
    lcd.setCursor(3,1);
    lcd.print("Counts: ");
    lcd.setCursor(10,1);
    lcd.print(a);
    yellow_blink(); 
  }