Certainly you may wear a sleeveless blouse under a jacket especially if you live in a hot climate. Never remove the jacket. Short sleeves choose them wisely. Give consideration to your career goals and your daily goals. Long sleeves create authority and a higher level of professionalism than short sleeves.
Short sleeves are more casual than long sleeves.
Use your attire as a tool to communicate your goals. Meeting with a group of powerful people - wear the long sleeves. Material A blouse is more powerful than a sweater. A casual top is less professional than a sweater. A one to two-inch heel closed in front and back shoe is the most professional.