Please don´t considering doing an at-home TCA peel if you have sensitive skin!!!! If you feel like you need a TCA peel to improve your skintone, get it done professionally by someone who really knows what they are doing, otherwise you really don´t know what you´re getting yourself into. My skin isn´t sensitive at all, so I´m comfortable doing peels (glycolic & TCA, which I always get from MUAC) by myself.
For sensitive skin I´d go for salicylic acid instead of glycolic acid since salicylic has some anti-irritation action, plus it works better in preventing breakouts. I´d start with a gentle leave on product that doesn´t contain alcohol (like Neutrogena´s 3-in-1 moisturizing treatment with 2% salicylic acid) and then try a weak salicylic acid peel or an Alpha-Beta peel.
So basically, my advice is to start out with a gentle leave on chemical exfoliant to see how your skin handles it. Slowly build up your tolerance if you can, and then you can move on to actual chemical peels, but always start out with the lowest possible %.