It's a known effect of Radiotherapy on the prostate, although not quite as dramatic as your case.
Alcohol, and fizz if it's a fizzy drink, are bladder irritants. What's happening is that your bladder is getting irritated and is contracting, making you feel like you need to pee. There are drugs to help relieve bladder spasms, so it's worth asking your oncologist or GP. They do all have side effects which you will need to trade off (such as dry mouth, which can make you want to drink more, which can make you genuinely need to pee more). There are also botox injections into the bladder which last from 6-24 months (and can be repeated), but I don't think anyone would consider that until you've had longer to recover from the radiotherapy when many of these symptoms will go anyway, probably at least 6 months.
Not quite so sure about the poo side, but may be triggered by the same thing, or by the bladder contractions. Poo urgency is also a side effect of radiotherapy, which should fade with time, although it does go completely with everyone.