My character is a Elf Drow (Weight: 95lb, Heigth: 5'3'') so, can I use a Panther (STR 14) as a mount or at least lift me up if I'm paralyzed?
A black panther is nothing but a leopard with a different color. Now, RAW aside, a leopard is capable of some astonishing feats:
In search of safety, leopards often stash their young or recent kills high up in a tree, which can be a great feat of strength considering that they may be carrying prey heavier than themselves in their mouth while they climb vertically. One leopard was seen to haul a young giraffe, estimated to weigh up to 125 kg (276 lb), more than twice the weight of the cat, up 5.7 m (19 ft) into a tree
So yes, dragging away a slender elf at 100lb + armor is childs play for a full grown member of this species. If it's a lot of fun being dragged by a large predator using it's teeth is probably another story. Don't expect to come out of it unharmed. You cannot drag something heavy without getting a good grip on it. In this case, good grip probably means it sinks it's teeth into your elf until there is no more resistance and no chance to slip from it's jaws.
Push, drag or lift You can push, drag or lift a weight in pounds up to twice your carrying capacity (or 30 times your strength score)
By RAW, strength 14 allows the animal to lift and drag 420 pounds. That's probably two or three slender elves, but at least your own character.
So no, riding your panther is not possible, because you are both of the same size. But a panther can easily drag you and your stuff vertically up a tree. By RAW and in real life.
A drow can't use a panther as a mount because mounts must be one size category larger than you (PHB p. 198), and drow and panthers are both Medium creatures.
A panther could drag you while you're paralyzed, but you're too big/heavy for it to pick you up in its mouth.