Okay, you were in a party with elitist jerks who would rather kick you out than give you some advice... or you didn't see what they said (if they DID try to help you).

Just so you know, it's a bad idea to nuke RIGHT away unless expressly asked to. I don't know how large your party was, but if it wasn't big enough to kill the mobs right away, the tank might have wanted to get hate. If they DID attempt to talk in party and you happened to miss it, or didn't respond, that might be why they assumed you were botting. The fact that you switched to healing when someone got low might have also increased their suspicions because bots can be scripted to fulfill certain actions under certain conditions. Is a player below 50% health? Switch to curing, etc. I didn't even know bots exist for FFXIV yet, though.

As others have said... I'm willing to assume your computer wasn't freaking out -- you were kicked from the party. In the future, watch the party chat more closely, and if you are new to something, be honest about it. Ask lots of questions. No one will fault you for asking questions, but they will fault you for making assumptions.

Oh, and if you were CNJ, they may have been expecting you to heal completely if it was needed. Again, it's dependent on the PT setup and who else was there.