Reinforce the message kicking is hurtful and not allowed and simply walk away from him. Let him cry it out and when he has calmed down a tad try and ask what is his problem and try to help him resolve it.
For the current bruises Ellen recommendations are perfect: Hirudoid Cream is wonderful and is also always available in our medical cabinet.

Personally I always find that Hirudoid cream works the best for bruises and sprains. I have it literally always at home for many many years and swear by it. You can just buy it over the counter at any chemist. Another good option is Arnica cream (which is a herbal cream) or a vitamin K cream.

Personally I would worry too much about bruises being embarrassing, although I don’t think it’s wrong to tell your toddler in a neutral way that it hurts. Rather I would focus on how you can help your toddler to express him- or herself. The developmental stage the toddler is going through and their inability to verbally express themself and manage their emotions makes that these outbursts occur. They need our help to express themselves through co-regulating and gentle love & care. It can help to teach your toddler some sign language

Icing the area for 5-10 minute bursts in the first 2 days, then keeping your legs elevated when you’re able. Hopefully this will ease the swelling and allow faster healing. Hopefully the little guy will stop giving you the bruises, that would be the best outcome. Hope you find something that helps