From 16 years on the other side of the badge...
"Racing" typically ISN'T what most people think it is. "Racing" statutes are usually written in a way that ANY speed-related 'competition' is racing.
Boiling smoke in a race away from a stoplight?...certainly that is racing. How about a side-by-side to see who has the highest top speed? ...again, certainly.
Also, two drivers beside each other playfully doing roll-ons from 30-to-40 mph...even if that is below the speed limit...THAT is commonly 'racing' because it is a 'speed-related competition'. In a lot of states, mere 'display of acceleration' is considered racing (a 'display of acceleration' is any driving activity where a vehicle is accelerated more than is reasaonably necessary to achieve a speed consistent with the speed limit of the roadway in question...even if you never get above the speed limit!).
Reckless driving? Well, that is typcially worded as any driving activity that reckelssly endangers others. Would 'racing' on a crowded street recklessly endanger others? I think a good arguement can be made that it does. Might the officer have charged you with something "reckless driving" that is a lesser included offense of racing (lesser included offense being a charge that is automatically an element of a more serious charge...such as tresspassing is automatically a lesser element, or part of, the crime of burglary)...Absolutely!!!
You assessment of the 100 mph speeding is accurate...if he "had to accelerate to 100 mph to catch you", that is direct evidence that you were doing LESS than 100 mph...no brainer there, but gettign that evidence in, in court is the issue.
So much depends on the specific wording of the statute in your state on racing and reckless driving, and getting the evidence in for the speeding charge, that retaining an attorney is probably the best investment that you could make right now.