How to structure the speech of one character when it consists of two linked but independent phrases

If you were writing a quote structured like this…
‘You were right Izzy!’, said Ted, ‘there is something we can do.’

… would be correct to have a fullstop after ‘Ted’ and a capital letter for ‘there’ (because it is two separate phrases) or would it be correct to write it as I have typed it above (because they are still spoken by the same person and so are connected, and a capital is not required)?

Also, would this alter if the example were something like
‘It’s no use,’ said Fred, ‘go on without me.’ (e.g. would that need a full stop and a capital after ‘Fred’, or does the above work?)

Thank you!