What are you feeding from the bottle? We used the TT vari flow and they are good with breast milk/ normal formula as they don't drip like some flows/teats so baby can suck to suit themselves more easily.
When my DD moved to reflux formula we needed a faster flow as it is a bit thicker and finally found the Avent variflow to be the only ones fast enough for her.
I would think the TT variflow would be fine for a 2 week old - depending on what you are feeding from the bottle!
What issues are you having, is your LO on meds?
Laura