I recently got bad whiplash on my neck and neckties have become painful to wear. However, I have a job that requires business formal at work. I would like to know what to do.  I've thought of trying bowties, but don't know if they are acceptable for a formal Washington/East Coast workplace.  Also, are there extremely light ties available - my normal weight ties make my neck sore after a day or two. 

Sorry to hear about your whiplash, that must be painful.

The best thing I can suggest is to go to a menswear store or to the mens section in a large department store and ask the Sales Assistant to recommend the lightest material tie for you. Off to top of my head I would suggest something in silk as being a lot lighter than the heavier wool blend ties. If you must wear a tie then this is probably going to be the best solution. 

I actually don't think it's the weight of the tie that is hurting your neck, it's probably the restriction of the collar and combination of the necktie with that adding pressure to your injury. You should speak to someone in your Human Resources department and make them aware of your injury. Then approach your Senior Manager to make them aware of your injury and ask them if you can not wear a necktie when at your desk and only wear it when with clients. This will reduce the amount of time you have to wear the garment and should hopefully assist in your injury healing quicker.

It's perfectly acceptable for men to not wear a neck tie in formal attire, in particular a tux without tie can look very stylish. It's more about the rest of your appearance that is important. Make sure you are highly groomed, your suit and shirt fits well and then take it from there.

Good luck and hope you're injury is better soon!