Yes you can get a TCA peel while on minocycline. Just avoid too much sun since you can get a little hyperpigmentation easier but with a hat and sunscreen, you will be just fine.
This should be treated with pulsed dye laser/vbeam to prevent scarring and derease the redness. Post peel/ablation skin care is needed, which includes a wound healing cream called bioshield and a topical growth factor, vitamin C, and sun protection. Please see a laser expert for...