Highly sensitive toddler, prone to meltdowns?

My daughter is 2 1/2 and has always been emotional. From day one, not a day has gone by without her having at least 2 horrible, terrible tantrums. Any little thing that upsets her, she screams and cries hysterically. She will pull her hair, scratch herself, and slap herself on the legs repeatedly. No matter how extra-sensitive I try to be to her needs, I can't prevent every little thing that may upset her, and I can't take her places because of her terrible meltdowns. I have a 4-month old, and when the baby cries, my toddler freaks out. She gets a toy stuck, she loses it for 30 minutes. If something upsets her she SCREAMS bloody murder and is inconsolable! I have tried everything and I am at the end of the rope. In fact, I am so far at the end of my rope, I feel like I can't take it anymore! If any other mom has dealt with this, I would LOVE to hear any good advice. Please help!