Well, let's start at the beginning again!
Glad you're OK (cos I haven't said that yet - sorry!)
Hope the bike's also OK.
Now, I ended up cycling past that way this lunchtime (not through the roundabout; but ending up on Chester street where you were trying to turn right). Looking at it (with a critical eye!) that street is very close to the roundabout.
Given the speeds that people do around there I'd seriously consider another route. Not sure how painful it is to go straight across the road you were hit on (Cambridge) though, depends on traffic at that time of the morning (I'm currently doing a left turn there so am not held up much, trying to get out of the mess on Oxford Road - and avoid being a naughty cyclist cycling down the pavement when the cycle lane dies on Medlock Street!)
Where are you trying to end up in Manchester?
Your other option is of course to go down Oxford Road and turn left onto Chester street that way; but I noted this morning they're doing some work to the kerb there on the new, fancy, cycle lane only left turn - given last time it took them months to clear the barriers, it might be a while!