Thank you to those who commented.
I reached out to my podiatrist and this is what she said...
Blisters on the feet following chemotherapy is a common side effect. When the chemotherapy reaches the feet it can commonly cause dry skin, redness, tingling sensations and blistering or cracks in the skin.
It seems in your case that your skin is not yet strong enough to tolerate any friction - when we wear sandals and shoes without socks, we get more friction of our skin against the shoe, hence the formation of blisters. In the warmer weather our skin dries out a bit more, which is why you will be noticing this happen more so in the summer months
Definitely one main way to help prevent this is wearing socks to help reduce the friction. Obviously in the summer this becomes a bit tricky as the weather gets warmer. If there is a particular spot in the foot that keeps blistering, we may be able to look at using some soft material in the shoe or sandal to help reduce the friction. In the clinic we have material called fleecy-web, which is great for helping protect the skin by reducing friction.
Another product that would be worth looking into is ENGO patches. I've attached the link to the website below. These are little pads that you place in your shoes where your blisters usually develop, and these work brilliantly to help reduce the friction. People who run events like ultramarathons use these often to stop them getting blisters midrace.
https://blisterprevention.com.au/blister-shop/