Is my H-1B Employer Specific? Do I need a new Visa when I change Employers?

From your email below it appears you currently have a valid H-1B approval. However, this approval does not correspond to the visa on your passport. Well, visas are not employer specific and therefore, you could travel and re enter with the valid visa and your current H-1B approval. A visit to the Embassy would not be required in this situation.