Elvia:
No one really knows what causes ITP. Many times with children, it can be triggered by a medication (antibiotics, etc), an illness or a vaccine. The MMR is known to trigger ITP and that is stated in the literature. Your daughter seemed to have a few things going on with the illness, meds and vaccines, so it's hard to say. Sometimes it happens for no apparent reason. Knowing the cause will not change the situation. As for giving her future vaccines, you'd need to discuss that with her doctors. Maybe they can give one at time or slow them down. Sometimes you can't avoid a drop no matter what you do.
ITP is usually acute in children, but it can also be chronic and might be something you will deal with for a while. If so, there are ways to manage it. It's difficult with a child so young who is learning to walk, but many parents have successfully managed to get their children through it. The fear will eventually get better as you learn more about ITP.
Children with allergies tend to acquire ITP more often because they are prone to autoimmune problems. Are there any autoimmune disorders in your family? MS, thyroid, Lupus, etc.? It tends to run in families since there can be a genetic predisposition. It's also possible that this is just a fleeting thing. Only time will tell. She's young and has a good chance of having it go away for good.