This chapter suggests the warring Toh are between Rand and Elayne... however it's terribly unclear, and in a later chapter it's inferred the conflicting Toh is different. Presuming the former, I think:
Killing Rand resolves her Toh to Elayne by taking from herself the thing she thinks she took from Elayne. She loves Rand, and removing him from the picture would cause her to suffer. This obviously conflicts with her Toh to Rand, as well as to Egwene where charged to protect and watch over Rand, and it's not the kind of thing that would make Elayne happy.
Killing herself resolves her Toh to Rand by returning that which he saved (her life). However this doesn't allow her to repay her Toh with Elayne (at least not directly), and though not mentioned, she's been charged with Egwene to watch over and protect Rand (for Elayne).
Later on, in Chapter 40:
Approaches Elayne with confession of her love for Rand and offers herself to Elayne for the repayment her choosing. In this chapter, she weighs her Toh between that toward Elayne and that toward Egwene (not Rand as previously expressed). While the offer in this chapter would allow Elayne to kill her (solution 2 above, attributed to resolving Toh to Rand, not Elayne), I believe Aviendha has come to this as the final solution as allowing Elayne to kill her (rather than killing herself) permits Elayne to shame/embarass/punish her fulfilling that Toh while at the same time fulfilling (or undoing) the Toh toward Rand as in Solution 2.
... I recall somewhere that Jordan was once asked about this and all he said was to read the book. Wish I had a better answer myself, but I am just a wetlander.