Whether a single 3-way, 2-position pneumatic valve (typically with a work port, an input port, and an exhaust port ‒ see page 3 of nationalpneumatic.com's pdf about valves) will suffice depends on information not given in the question. For example, if you can turn the compressor on or off at will, and if it will hold pressure when off, you can attach the balloon to the work port, the compressor to the input port, and leave the exhaust port open (or put an exhaust silencer or rate control on the exhaust port).
If, however, you are using a reservoir and need three settings – balloon fill, balloon hold, and balloon exhaust – you will need to use either a 5-way, 3-position valve with center off (see eg youtube.com about Closed Center Valves), or a pair of 3-2 or 5-2 valves. (The 5-2 valves would be used as overqualified 3-2 valves, with extra ports either blocked or left open as necessary.) Using two 3-2 valves X and Y, on valve X attach the balloon to the work port and leave the exhaust port open (or silenced, etc). Connect X's input port to Y's work port. Connect Y's input port to the compressor, and block Y's exhaust port.
The “VIAIR 12V 120 psi Air Compressor” mentioned in a comment is an oilless single-piston compressor. As well as being sold at the robotshop.com site, it is marketed as part of a roughly twice-as-expensive air system, on Amazon and other sites. A single 3-way, 2-position pneumatic valve should work ok for balloon air control if used per paragraph 1.
Somewhat-less-expensive compressors that will work ok for initial experiments or for light duty production include Harbor Freight models 61788, 69284, and 4077.