Retinol can definitely be beneficial even though you're using AHA and BHA. The key is to start low and slow, so you could look for a retinol with a low concentration and slowly incorporate it into your routine.
I started earlier this year with the Olay 24 hour retinol, and would say it's quite gentle as it's in a formulation with lots of emollients and other ingredients. Unfortunately Olay doesn't disclose the percentage, but I've not experienced any irritation or sensitivity with it. I've got The Ordinary lowest percentage one in squalane for when I finish my current one, but have also seen that the granactive retinol in squalane recommended for beginners.
Just make sure you give your skin recovery days without any strong actives, and don't use AHA BHA on the same days as the retinol. Good luck with your retinol journey!