And that is exactly what you were doing wrong.
Beginner in Killing Floor is like playing against angry cats. At worst, you'll lose one guy because he got careless and tried to fight off fleshpounds with his knife. At best, no one will take any damage throughout the entire game. If I were to play Beginner with my level 6 Commando, I could probably kill the Patriach with a machete.
On Normal and Hard, my squad absolutely needs our dedicated medic, especially with the Gored Fast mutator running. Without him, we start getting screwed over pretty quickly.
If the game's difficulty levels weren't so drastically different, I'd suggest playing on Normal. However, that generally isn't a good idea with a low-level perk. Find some experienced players and try it out as a team. Try to sit back, let them do the heavy lifting, and work on levelling whatever perk you'd prefer to play as - if you're planning on playing Medic, this is a perfect situation for you, especially if there aren't any other medics in the game.
Of course, throughout the match, you should also be looking for good playstyles and how the specimens work, assuming you're still new to the game. Look for good hiding places, figure out where the trader spots are, and get a good feel for the weapons.
The game gets pretty stale after a while, but it's good for some semi-mindless fun in between more intensive games.
...those that did just healed themselves.
This is one of the reasons why a Medic should play with friends. If you know people well enough, it's easy to convince them to hold off self-healing to let you level your perk. Hell, I even jump off cliffs every now and then just so our Medic can get some more heal points in.
On top of that half the team was level 3-4.
Well, to be honest, that half of the team was a bunch of douchebags. At level 3, you should be playing Normal. Beginner becomes a carefree cakewalk at level 2, maybe even level 1.