I am not a doctor, I just grill mine for all the information I can get. I have hypothyroid, I was told that my tsh needed to be under 2 to feel ok and be able to lose as close to normally as I was gonna get with this condition (long term, mom had it). They got my TSH down below 2, over 9 months, to a wonderful 1.75 and I feel much much better. I know folks that have the opposite issue with thyroid have different goal ranges than those with hypo from my questions I ask.

I dont know too much about the low end of the range because I haven't been there. I have learned so much to help myself by asking my doctors for answers that cut through mullarky. I suggest you ask him/her questions about it and if your phone calls are left unanswered and you are local, go there and request a follow-up appointment or to maybe speak with the physician they consult with.

Your numbers are a bit confusing to me as your tsh almost seems hyper while the t4 seems hypo but I am no expert by any means. I am now borderline hypo tsh 3.6,was 4.3. I feel fine and have been losing slowly through diligent tracking. I just came off a bout of hyper from thyroiditis. Not fun. Good luck and find a good endo. My gp wouldn't even begin to treat me when I was hyper she said it was out of her area of expertise. My endo has been awesome and I feel like I am in very good and knowledgeable hands. Good luck!

Good luck! Keep us posted.

This is something that many, many people go through after RAI. It is going to be a battle for you until you find a doctor that knows what they are doing. Your TSH will stay low for years, maybe forever, when you have Graves because of the antibodies. That's not to say it can't rise but antibodies supress TSH levels. The problem with this is that most doctors dose off of the TSH and it's just not accurate in your case.
You need to be monitored by the FT3 and FT4 levels. This is the only real indicator of your thyroid status. I would find it really hard to believe that you don't need to be on meds. You may be able to go for some time on T4 meds (Synthroid, etc) but eventually you will need T3 (Cytomel, etc) also.
There are a couple of good resources to check out and educate yourself. I hate to say it, but if you don't you may end up feeling really miserable. Doctors in general are horrible at dosing. There is a website run by Elaine Moore. Just google her name. She had RAI and really regrets it because it made a huge impact on her life. She has lots of info (and books) on her website and a forum that only she replies to. If you write in with your info, she will post back in a few days what she thinks you need to do. She is excellent at advising on levels and meds.
The other one is llivingwithgravesdisease.com. This one is a community forum (like here) with lots of great info and links about RAI and Graves. Anyone can post so you have to take the advice with a grain of salt, but there are a lot of really knowledgeable people on there.
I hope this helps! I don't have Graves, but I was hyperthyroid for 8 months due to an infection in my thyroid. Now I am hypo and on Synthroid. I have to battle my doctor every time I go and I still don't feel well. It is an uphill batlle!