Products with hyaluronic acid will have a temporary visual plumping effect on those lines, that's your best bet to help without resorting to surgery.
Some people also have minor success with rosehip oil on fine lines, it helps to soften them a bit.
Another temporary solution is the eye masks you can buy - a few brands do them. I have used these before when tired to good effect, the DHC brand is good and much cheaper than the high end ones. You look ridiculous wearing them but when you take them off your under-eyes will look fresher and plumper!
None of these are proper solutions like botox though - they won't reverse the signs of ageing in the longterm, they'll only visibly smooth and plump the area for the day after applying them. Better than nothing though - and very cheap options!
If you're truly dehydrated in your skin I'd also recommend upping your water intake and layering hyaluronic acid products over a spray of water (like those spring water sprays you can buy for skin), so that you effectvely help lock in that water to your skin. Make sure you aren't using products that are too harsh and drying on your skin, too, and that you aren't dragging your skin too hard when washing your face, moisturising etc.
