Long fight with fleas

I am an OAP living alone with my 10-year-old cat. I've been struggling to get rid of fleas on her. I haven't seen these before and she also has what look like rice grains coming from her bottom. I've been using a pet shop recommended treatment but I think the fleas are resistant. Can you advise?

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It's very useful that you have seen fleas, and also what look like rice grains, although these are probably tapeworm segments.

Early products for parasite control were not very effective. Modern products, including those prescribed by vets, are licensed, meaning when used correctly they are safe and very effective.