No not all of them are "required" to be considered a TOS case.
A mix of those symptoms are the usual.

And at the beginning of TOS the symptoms can often move around- and that really confuses the non TOS drs.
And the severity can fluctuate with uses that aggravate it.

Delayed pain is a usual sign- the pain will get worse hrs after certain uses and take days or longer to recover from.
Constant tight neck muscles or easily strained neck muscles
tight or strained feeling in the forearms

Oh and look in a mirror and check to see if your shoulders are level or one higher than the other and then if you can or have a friend check your hip bones for evenness.

If uneven - check that useful sticky for the chiropractic links - it explains how the body will try to compensate for crookedness.
That was a part of my TOS cause then adding in the yrs of repetitive work.

I don't have RSD but have read a lot here from the group.
They can help with the differences too but I'll try.

RSD
Painful burning skin, extremely sensitive skin - to touch, fabric, even air or light breezes will be painful, lots of swelling, skin color changes, texture changes

TOS
loss of fine finger coordination in hands, upper body muscles {neck, shoulders, back, arms}that tighten up easily or ache constantly, nerve zaps, bruit {you can hear your own pulse whooshing sounds}, tendency to get triggerpoint knots in muscles, blood flow in arms can get stopped if arms are raised to certain positions, can present as many different RSI injuries at first.
The vascular system compressions can cause swelling for TOS too - but usually not as extreme or colorful as RSD.

The chest pain comes on usually if you get a major muscle spasm of the chest muscles.
I had it once from extreme physical overuse at the time - took months to recuperate from those.