An additional half GB of data to get to the end of the month (based on your current use patterns) would cost you an additional $25 this billing period. Increasing your plan to 4 GB/month will add $20 (or a portion thereof) to your bill. You can only change your plan once per month, so if you are in your first month, I believe you could not change until the beginning of the next billing period. If you are not in your first month, you should be able to make a change. I expect the cost and the data would be pro-rated to your next billing date, but you should call Telus and ask.
I know it's tough to wait when you have no data left, but what I do, even for upgrading my phone, I wait until the last day or so of my billing cycle to make the change. It takes a little planning ahead, and waiting sometimes, but it saves a lot of billing fuss, so the planning and waiting are worth it.
I would just give Telus a call and see what they have to say.....
When I got my first phone decades ago... there was was an opportunity to change in the first weeks as new users don't have any idea how much data they want to consume. Of course... things may have changed since then.
Otherwise.... home and public wifi is your friend until your month expires. Look also at TelusDirect wifi hotspots.