I am leveling the same way you are asking in this question :)
As a medicine Operative, your biggest damage comes from a few things:
- Corrosive Dart
- Overload Shot
- Fragmentation grenade (if there is more than one target and you are not crowd controlling the other units).
I'm currently level 41 and this is what my build looks like so far: http://www.torhead.com/skill-calc#401MffbzGoRzMZMZoM.1
The key to this build is the 3 talent points in medical engineering. It will constantly provide you free Tactical Advantage buffs that you can use on Surgical Probe while still doing damage.
For large groups, simply spamming Fragmentation grenade gets the job done quickly and efficently.
For fighting harder mobs or just a single target, start off with a Corrosive dart, Backstab, shiv, overload shot, then repeat when they are off cooldown for damage. Maxing sure that the Kolto probe buff does not fall off and that you always have Stim boost up. Should you run low on energy, use Diagnostic Scan a few times on yourself or Kaliyo, whoever has damage to them. Every little bit of healing helps and the DS crits will give you energy back as well.
The healing aspect for both encounters is handled by the Kolto and Surgical probes. I start by using one Kolto Injection to get my healing buff up caused by Medical Consult, then I drop 2 Kolto probes on Kaliyo, then pop Stim boost when Tactical Advantage procs off of Medical Engineering.
The start of the fight is done with the healing aspect because you want to make sure that you are procing TA so you can get "free" heals on Kaliyo by using the Surgical Probe while saving your energy for your damage abilities (Backstab, Shiv, Overload shot). Kaliyo is only there to hold agro while you kill the mob. At level you should be able to kill most with 1 Backstab, 1 Shiv, 2 Overload shots on green/yellow enemies.
You can see in the talent tree that I have only a few talents outside the medicine tree that increases the damage of Shiv and Backstab, my main DPS abilities. But aside from that the large majority is in the medicine tree.