I would definitely say that having all of that in a week is crazy early, but hey, maybe your natural T levels where higher than mine. Who's to say? But I would say, don't worry about it. That's all normal, it just took me longer than a week to get to that point.
But yes, needing to jerk it out that often is totally normal, and I would say that sensitivity is normal as well - and like with most others on T, it didn't stop me either. I wasn't at all unusual for me to have to take care of myself 6 to 8 times a day. Seriously, it really was that bad (( And I'll continue the horrible trend of mentioning that the built in lube of girly parts is certainly nice, I don't have to keep lotion by my bed ))
Being sensitive while your hard is normal.
The clit has many more nerve endings than the tip of a bio-male cock, and even men experience sensitivity while hard if they're walking.
I don't think that it's anything to get worried about, unless the sensitivity increases to the point of pain.
Then I'd say something to my doctor. Definitely.