you have a shoddy installation job and poor vinyl also. Yes, there are some bandaid products out there that will fill the seams for you but the laying down of the curled edges could be a challenge. I would get a hair dryer and limber up the edges and then apply some adheasive after cleaning out the floor area then using some sort of weight to hold down the edges. This should work for a short time.
I would have in your short term plans to rip this up and lay down a good quality vinyl flooring that is thicker and have a pro do it.