I think the missing paint is from the chain recently gouging away at the paint since there isn't any paint missing on the opposite side; and where the missing paint is, on the top of the chainstay then angling down as it goes toward the rear was definitely caused by the chain.
I would try a 28 and see what happens, but only if the store will allow you to return the tire once it's been installed on a rim if it doesn't work...usually they won't. If you know someone who runs 28's on their bike you could borrow the rims. The tire not only has to clear the rim but it also has to clear the brake calipers.
A good tip I learned: look at your existing tire in the frame and figure out where the point of tightest clearance will be. On the front wheel that's obviously up by the brake and the fork. On the rear, it is probably down by the bottom bracket on the seat stays.
Then, take your allen wrenches and progrssively slide them between that point on the tire and that point of the frame. Start small and work your way up in size, eg: 4mm, 5mm, 6mm, etc. If you can fit 6mm, for instance, on both sides, you have an additional 12mm of clearance. So if you are running a 25, and you can fit an additional 12mm total, you should be able to fit a 28mm tire or even larger.
I aim to have at least 3-4mm of clearance on either side of my tires - to account for a bit of wheel flex and occasional mud.
I also own a set of digital calipers, pretty cheap on amazon, to get an accurate tire size to base my initial measurement on. The printed tire width is often not what the tires actually inflate to, particularly on wider rims (18mm internal width +).
Why not ask at a bike shop? Most front road wheels are more or less interchangeable unless they have a disc brake or a bolt on front axle. They could easily take a spare and clip it in. Of course, you'd then have to buy the shop's 28mm tire.