I ride that kind of distance in the Uk; you don't need any sport cycling equipment if you ride at a moderate pace. I could do it ordinary street clothing but I prefer a wicking T shirt. My favourite is material is merino wool , it is more comfortable and less stinky. You need a good windproof and a waterproof for when it rains. Rainproof pants are good in a downpour. I use regular runners training shoes but in the cold/wet I add sealksinz waterproof socks. A neck tube/buff is useful for fine tuning insulation. Thin woolen sweaters make perfect midlayers. Dont forget gloves, they keep you warm and protect your hands from any sldie across the road.
If you feel the need to ride more athletically note that you will have to cool down and wash down at the other end which will eat up all the time you saved by riding faster over such a short distance.

Most bikes will do the job but make sure you have a suitable set of gears, eyelets for mudguards/fenders and luggage rack and the bike is roughly the correct size. Modern tyres are a lot more puncture resistant than they used to be. Schwalbe Marathon Plus are the toughest of all but there are others. Puncture resistance will give you peace of mind and help your punctuality at work so it is worth getting good rubber.
Most LED lights are good enough for the task but carry a spare rear blinkie.

I have no advice regarding your medical condition but note that if someone is found lying next to a bike, the assumption is that either they fell over or were hit by a car. Make sure you have some medical info in a prominant place, not just a bracelet underneath all your winter clothing. Maybe write it inside your helmet.



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