Are you doing it yourself or professionally? I don't believe TCA cross should be done at home, but that's just an opinion. Besides, your scars look more box car. Needling needs to be done in sessions. One treatment wont do much at all. It definitely is something to consider, recovery time isn't long. You can get started on sessions. I also think subcision would be great to consider.
A TCA peel would result in a little bit of texture improvement, but wouldn't do anything for the medium depth scars. It wouldn't hurt, there would be some improvement in the overall skin smoothness. I like TCA peels, I recommend light TCA peels for most people but know what to expect. It's more for hyperpigmentation and texture.
Needling only has like a one to two day recovery time at home. You can get into the routine of at home needling anytime. I would do it every 3-4 weeks. Give it time to heal in between. If I were you, I'd get a peel done for the two weeks you have to heal, give it 4-6 weeks and start needling every month. I'm kind of a slow and steady pacer. It's ultimately damaging the skin, got to give it that healing time in between.