I've heard a man shouldn't wear anything on his left arm (as a bracelet, watch, etc) while having tefillin tied on. If this is true, would it be completely wrong to wear a red string on the left arm (where it should be) if one puts on tefillin daily?
According to Kabbalah, the red string should be on the left receiving side.
Hakham Ovadya Yosef z"l rules explicitly in Yabia `Omer (Orah Hayyim 2:2) - citing the view of the Rashba - that the concept of a hassissah only applies to the bayith and the upper arm, not to the straps, and especially not on the wrist. The question there is regarding a wristwatch, but it would by extension apply to anything being worn on the wrist.
[As for the red string itself, the concept is completely without source or basis in Hazal or even the kabbalah. It was something started in a couple of families not too long ago and has caught on as a money-making superstition. Check it out for yourself.]
Hope this helps. Kol tuv.
I don't see why one couldn't wrap the strap of the t'filin under the string (unless it's very tight). That's what I've done with hospital identification bands. Then, to answer your question, "would it be completely wrong to wear a red string on the left arm… if one puts on tefillin daily?", no, I don't see why it would.
But consult your rabbi if this is a practical question for you, rather than relying on what you read on this site.
The Mishnah Brurah (27:16) says to not put anything between the tefilin straps and the skin. This implies that when not wearing the tefillin straps, you are allowed to put something there.
