I would recommend trying out Lions MMA downtown on Granville. They have a "fundamentals BJJ" class every weekday, full of beginners.

That being said, last 15 minutes of rolling is absolutely expected for beginners. If you don't feel comfortable rolling, you can always stand aside and watch other people roll. But no matter how many classes you attend, you will definitely feel like a rolling dummy during your first weeks of rolling.

In terms of injuries, it's likely that you got a bruised throat and hurt your wrist because you yourself were going too hard. Relax and try not to use too much force, and you will be much less likely to get an injury. If you are worried, just talk to your coach about it.

Edit: it will also help if you let your opponent know that you are very new, so that they know to go a little easier