I mean, 3 dates and no sexual escalation? You are pushing for that friend zone. Leave kisses on the chick for your aunt.
If you want to do something (like kiss her), do it. Do not hesitate. Saying to her "I want to kiss but I won't" translates in her brain as "I want to kiss you but I am afraid". Big no no.
To your question, no, you did not overreact. You were upset (rightfully so), played it cool, and took a step back to reassess. You did right.
Her giving this other guy her full attention for a significant amount of time that night is a sign of disrespect, disregard, and perhaps even mind games. She has clearly shown interest, but you have not finalized it, and the longer this goes the more risk you'll run into of loss of interest, friend zone, and lastly disrespect.
As a man, you take action, if you want something TAKE IT! It is partly what makes us men. We act on our true desires