Hey, I had the same problem for the entire time I've been on T (abt 2.5yrs).
I mentioned T-levels to one of my buddies who has been on T 5+yrs and has had most of his trans healthcare done in NYC. He told me there is definitely a difference in T-levels in the blood based on when you do your dose and when the labwork is done--trough levels (lowest amount of hormones present in the blood) and peak levels (highest levels present in the blood). I remember it because it's similar to the way ocean waves work. :p
For half of my time on T, I was getting labwork done on trough days (a few hours before I dosed) and then I switched to peak days (3 days after dosage) and it really worried my doctor that my levels went from 'normal'* to 'above range'*. Her initial reaction was to lower my dose substantially, but I did some digging and brought to her attention the pattern I just mentioned. I compromised with her, lowering my dose, and still get labwork done on peak days. But my levels are consistently 'high' and I haven't had any adverse side effects, and she hasn't been concerned.
I accidentally did a double dose of T during my first six months, and it was not fun. All the daily effects I'd experienced on T--increased energy and appetite, increased libido--were increased ten-fold. I couldn't stop eating, I had jitters and shaky hands in addition to needing to be in constant motion, and I think I got about 4hrs of sleep a night. It took about 72-hrs for the worst of it to wear off, which is about the time I really started keeping excellent documentation of when and how much I dosed, and consistently video documenting any physical, mental, and emotional changes I experienced. I recommend this as a safe-guard in case you change your dose/start any other medications or supplements and need to compare any side-effects.
As for researched over-exposure, my doc mentioned liver damage, as well as the stereotypical "'roid rage" examples--aggressiveness, anger, severe acne, thickening of the blood, among others. I never experienced any of those things, but that's not to say it doesn't happen. Your doc should be able to provide you with resources if they feel you're at significant risk (and even if you aren't!).
I've had some really good discussions with my doc about where she gets her data for hormone ranges. I'm always skeptical of data collection, because there are so many variables that can influence a person's hormone levels (age, race, ethnicity, diet, geography, genetics, overall health, etc.) and I told her frankly that I needed more information about where she got her data before I changed my dose. And honestly, her sources were kinda archaic. I know there's a really awesome trans clinic in NYC (Callen-Lorde?) that could be a great information resource for you and your doc!
Good luck!
*mod edit- no dosages please