In my case, I have had the opportunity to study the body enough to know what is happening and what to look for (I'm a reflexologist and certified massage therapist). I realize not every mom has this in their 'tool box', tho.
However, I think you did your son an injustice by not checking it with the doctor right away and threatening the flu shot... that's just bullying him. Siblings do not always get along and this is a younger sibling, therefore do you truly expect the younger brother to be truthful about big brother's situation or to truly be able to assess it correctly? Especially if big brother was walking slower and didn't need to limp?
Sometimes a hairline fracture can occur in a sprain. If there is swelling ~ there is stress or trauma in the area - indicating an issue. Do you have a medical degree to assess the situation? I don't and I would be taking my son in to the doctor~ all the while treating him to the best of my ability to a) keep him calm and b) halt the swelling, pain and bruising even further to allow healing to come faster.
I feel you just taught your son that a) you don't trust him about knowing what is going on with his body and b) you are indicating that he is lying about something that may end up being serious (and how would you feel if there were a fracture? My guess is pretty crappy in the long run, right? I know I would.), and c) that you are basically not listening to him when he may need you.
Yes, our kids may like to pull the fast one over us. My son would prefer to stay home and will tell me he doesn't feel well. However, if he doesn't hit a range of symptoms~ he doesn't stay home. As I work his feet in the morning, I can verify what is going on in his body by how sensitive these area's of complaint are.
But I also feel if you talk daily with children, get down on their level and chill out or play with them... alot of this can be avoided.
I truly hope your son is okay. Sprains and twisted ankles do hurt and a sprained ankle takes just as long to recover from as a broken ankle (keep that in mind. All those tendons & ligaments stretch and need to heal.).
Edit: As a reflexologist, I can tell you the foot is complex, as is the ankle. There are 26 bones, 107 ligaments and 19 muscles in the foot alone. As we use our feet daily, any injury on the foot will upset the entire body and affect it in another way, even by causing another pain symptom.