A.J.
For the most part, you are being very understanding, which is good. However there is a fine line between being sensitive to his needs, and letting him rule by tantrums at times.
For example, because we don't allow tantrums in our house after about 18 months of age, we may have to leave disappointed kids outside the bathroom door from time to time for a few seconds while we pee or take a shower, but having a melt down over it isn't an option. They know discipline would result, so they buck up and wait until we're out of the bathroom, can pick them up, etc. Same at bed time. Tantrums are not an option there either. Freaking out and peeing on oneself if mom refuses to come into bathroom. Not an option. If you are going with him every time to avoid that melt down rather than disciplining the behavior, he will keep doing it.
It would save you lots of headaches to nip the fits, even though it's hard to be firm in those moments at first. He will get more confident and happy once he is forced to be a bit more independent and control his fits. He'll still be sensitive and love you to bits, he'll just start to behave better which is a load off everyone's plate. You'll spend a lot more time on fun with him when this stops.
My friend has a son who was super sensitive and clingy and acting like you describe at 2. She and her husband never disciplined it, just nurtured it and kept on his good side as best they could, and now at 4, he still acts that way and it's NOT cute anymore. They have "that kid" none of their friends can stand to be around, and it's not the child's fault.
Believe me, my 3rd, who is now 2, was born angry, and now, thanks to firm, calm discipline, she will control her fits and it has saved my sanity because technically everything "upsets" her but that doesn't mean she's allowed to have fits.
If you have him potty trained so young, you do have the fortitidue! You can do it!
If you want advice on how to nip the traumatized behavior and fits, this book is great Back o Basics Discipline by Janet Campbell Matson.