A little bit of exploration of the dings will help, the blue part only has surface creases no worries there.
get your finger nail and scratch at the damage on the white part of the board, if you only get paint particles then the damage is only cosmetic, if you scratch up fibre particles then it could be more substantial.
Solar epoxy resin will fix it as long as you haven't severely compressed the foam.
If the foam was severely compressed the the blue part may well have been separated with a fracture line in the harder plastic base.
I Imagine the damage was caused by tying the board on too tightly .
I would suggest broad straps rather than rope or elastic straps, most people are capable of pulling tie ons too tight on soft board, even regular boards can be damaged by over tightening.
A few more tips, you probably won't need a base coat as the "non" slip surface will take the wax easily, just match the wax type to you water temperature and wax as suggested by Waikikikichan.
You need to spend more time on this board before your progress to another board.
You need to get your grumpy girlfriend surfing or look for a trade in to one who does.
Strangely the grumpier she gets the more likely one of two scenarios will happen;
You will capitulate and stop surfing
or you will continue surfing to avoid grumpiness and a new relationship will be required..
Uncle Jaffa's advice for the potentially lovelorn surfer to be
Quite few of the forumites have taken option 2, the former forumites who have taken option 1 have never been heard from again.

I've taken up troll hunting just for fun, instead of a rifle I'll just use a pun! 冲浪爷爷