Use a ruler to measure from the top of the tire to the underside of each brake. On the front look carefully to see if the underside of the fork may be an even shorter distance. The shortest distance measured is the amount of clearance you have to work with. To go from 23mm to 28mm you need 5mm. The sides of the tire will expand 2.5mm each. How much space you leave after going to a biggers size is up to you but 2mm would be pretty tight.

To complicate matters, not all 23mm tires are 23mm. Measure the width of your present tire and if it's 22mm than a 28mm tire will need 6 extra mm of clearance.

There is a possibility if your rims are narrow that you can't get an inflated tire past your brake blocks when installing a wheel. If you take the tire off a lot to use a car rack this might get old. I recommend carrying a track pump in your car and a frame pump on the bike since you'll pumping up tires frequently.