I’m trying to get to know people so end up speaking more. But then I go home and feel really self conscious and awful.
If you're trying to get to know people then you need to let them talk. Do you mean you're trying to get them to know you? If that is what you're trying to do, maybe ask yourself why you want to be noticed or validated or acknowledged.
Feeling self conscious and awful might mean you are talking out of nervousness or anxiety and when that feeling passes you have more self awareness. Beating yourself up after the fact will hammer your self esteem, which might be low to begin with (hence the need to be noticed or acknowledged).
I am able to stop talking when appropriate (e.g., in meetings, client work) it’s just socially I struggle, it’s like I get carried away before my brain is like STOP. it’s difficult to explain really.
I like the advice upthread to practice really listening, not the half listening-half forming your own response thing and waiting for the chance to jump in and talk that many people do. Try a mindful approach to your daily interactions. Remind yourself when you spot a colleague that you are to exchange morning greetings and a smile, and no more. Try to practice this daily. Keep a journal (on a notes app for instance) so you can keep track of all your interactions and mark them on a scale of 1-5 where 5 was a brief comment or greeting and 1 was buttonholing someone for half an hour.
It's sad to end up berating yourself or feeling your mouth ran away with you. Try to be kind to yourself, and don't despair. You can get on top of this.