If size is the issue, then getting a used bike is the way to go. Since you want rack eyelets, something often lacking with true "road" bikes, consider something billed as a touring bike - these are bikes that are similar in geometry to a road bike, but have higher handlebars and are built for carrying a load. If you ride one of those every day then you'll find the racing bike feels like riding nothing at all. 3.5 miles isn't very far and commuting isn't a race, so I'd be less concerned about speed issues in a commuting bike. As someone said, think of it as resistance training.

If some adjustments to the bike would make it fit - raising the bars and seat, assuming the top tube is long enough - then it's mostly about maintenance and your money would be best spend on racks and panniers. Check around to see if there's a community bike shop in your area - they can teach you a fair bit about bike maintenance which will make your current bike a much nicer ride.

For a short commute where you're not likely hauling a lot of weight, the only thing that's particularly important in the racks and pannier department is waterproofness. Otherwise low end inexpensive components should do the trick, and it will save your back the workout.