According to the pic your saddle might be as high as it would go, but luckily enough not as far back as it would go. In terms of back & forth adjustment of saddle I recommend conservatism.
And for what that can be gained from the pic the set up seems fairly average for a reasonably experienced rider, top of drops a little lower than the saddle. The flat bar of my commuter probably ends up somewhere between your tops and your drops. But yeah, for a novice rider, that's a quite straining position to be in.

Where to go from here depends on what you want, and how you cope with riding on the tops. If riding on the tops is OK, then, as suggested, a moustache bar could be the easiest way forward, requiring the least amount of associated replacements.

But I'd suggest getting a steerer tube extender instead. Slap one of those in and you should get the bars a good few inches higher. Then you can ride in that position until you've gained enough strength to be able to start lowering the bars towards their current position again.