Swell, not sure why you received 2 bills back to back, but I had a first bill after putting solar on, when AGL didn't get the data right for some reason, and issued an adjusted bill with some credit applied.
Your bill should show solar feed in.
Re high bill(s) . . . one thing to be aware of is when you had solar installed, you might have had a meter upgrade to a digital meter, and an old analogue meter might have been on fixed / single tariff.
Retailers will typically just change people getting new digital meters to a TOU (time of use) tariff, which can be awful for some people that don't use power during the day, but at night when they get home from work and power is at its peak (and solar isn't covering that !).
Did you get an app with your solar to give production / consumption reads ?
Did they show you through this ?
You should see solar feed in on your bill, but AGL should have been notified (like your electricity provider) to get everything right in how it's all working together.
Wiring can also be done wrong, sometimes incorrect wiring can ADD solar production figures to consumption, but not sure if that is the case with your issues.
I had these 2 above happen to me, where I ended up notifying AGL, and my solar guys wired up some of my system to single phase and not 2 phases (of our 3 phase).
You can download data from your retailer (AGL) and provider (differs from state to state), and looking at the solar column on the CSV spreadsheet, you should see figures for between the normal production hours, say between 0830 and 1600 should be something there even in winter.
A simple reading of your data solar figures should show some figures which should align with you system size, weather conditions, shading etc.
If there are no figures there, you will likely have an issue with the solar install.
