This medic deck aims to accomplish the following:
1. Keep the team alive. The deck has a baseline of healing cards that will keep your team in the fight.
2. Stay mobile, stay firing. SMG cards help with this, as does Run Like Hell/Hellfire. Don't be afraid to kite specials while keeping common ridden off of you
3. Minimize the drain on the team's ammo/weapon resources. You have infinite secondary ammo, and your primary uses the least-desirable ammo type.
Preferred weapon loadouts are either Any SMG + Deagle or Magnum, or else UMP + TEC9 or Glock 23 (auto or not). Essentially, if you need more range, take a Deagle or Magnum as your secondary and abuse it as much as possible when you have Ammo Stash. If not, the TEC-9 counts as an SMG as well, and benefits from Speed Demon (thus offsetting the Ammo Stash drawback). The Glock 23 Auto does not count as an SMG, nor does the Beretta Burst.
In terms of combat duties, keep things off your Jim if you have one and focus on killing basic ridden. If you don't have Ammo Stash yet and both your weapons use Pistol/SMG ammo (you don't have a Deagle/Magnum), a secondary pistol like a Glock 23 or even a 1911 is a good choice for conserving ammo. Once you have Shredder, empty clips from a high ROF weapon at specials to help get them killed. On boss enemies it should be easy to get Shredder applied and maintain it until the enemy dies. If your team is dying around you, remember that the deck has minimal passive defenses and that you need to evade using movement speed. I have successfully kited large groups and worked on killing them myself, saving a run. If you have Hellfire + Ammo Stash, you can fire your secondary for a burst of speed.
To tweak the deck for more healing/utility, you could consider adding Poultice (works on pills btw), Group Therapy, or even Rousing Speech (not recommended if you have extra Offensive Slots, at least IMO.) Needs of the Many is a strong card but its drawback with this build will require you to play even safer and more evasively, so it's not for everyone. Chemical Courage is another strong option but will likely work best if your allies are the ones carrying (and dropping) the medkits while you hold pills; it's just hard to get someone to drop pills in a frantic situation. Saferoom Recovery is also pretty nice but it sometimes feels like neither the ammo or Trauma reduction gets much value.
For more damage, you could consider the humble Mag Carrier as it affects all your weapon choices, or perhaps Hyper-focused if you're playing more of a Deagle style or if you're on Act 4. I also think In The Zone could be a nice addition whether you're Deagle sniping or firing into hordes with a Tec-9.
Scar Tissue is a decent defensive option on Veteran and below. If you have a melee with Vanguard or you are using Poultice or Chemical Courage, Numb can be a better all-around option for dealing with specials.
Adding standard Stamina/Movement cards like Cross Trainers and Superior Cardio is also an option.
I find it difficult to live without Shoulder Bag or Support Scavenger. Money Grubbers is objectively a good card that gets better if your team can fit in a Copper Scavenger somewhere, but you should have enough money most of the time to restock your supplies without it (if not much more than that). Pick Medical Professional only once you're ready to start buying Medkits (and preferably, you have at least one Support Item Upgrade by then).
Though Highwayman affects pistols, it feels like a serious trap because it happens so infrequently. Combat Knife is highly discouraged as Doc's knife attack costs twice as much stamina as the others, plus your default bash has a wider arc and can serve to protect you.