The main challenge of healing in solo is you have to manage khem. Once he get his threat generating AoE, you can neatly group enemies on him, and use force storm to take quite a few out.
The basic DPS of the sorc is very good, and nothing stops you from using it PVE, and just spiking heals when khem goes down. At all time, you can stop damage to him with your shield, the time the heals gets in.
Force Surge, is a must, since it allows you to regenerate your force very quickly, while keeping a very good healing output.
For the note, my sorc is the toon I like the best at PvE. Soloing champions at level, most heroic 2+, and some heroic 4 with 2-3 level above.
I've of course, geared Khem well.
But manage your CC, and direct khem, find a good balance between Healing and DPSing, works like a charm.
Just be aware you do not have the DPS sorc bonus to force regeneration on your force attack, so uninterrupted DPS WILL deplete your force quickly.
If you have a possibly long battle in front of you, moderating yourself is your best bet. Moderating your heal as well.
I have very set chains depending on what I'm aiming for, may it be the best healing output, or simply low-cost heal to avoid the more costly chain. In this, Force Bending, the proc given by resurgence, is a must of your managing. Its a near sure yield of Force Surge if you wish it, or allows Dark Heal to be a low-cost alternative to Dark Infusion, which any non-heal spec do not allow.
Versus champion, I normally spend 2/3rd of my time on the heals, mainly to access force surge and avoid bad surprise, and I unleash a short DPS rotation every 15 sec or so.
In those 15 sec, I normally simply renew my companion shield, cast Resurgence to apply the armor boost, and either apply Innervate or a bigger heal if needed. Keeping an eye out on bleed, poison and other DoT you can remove with Purge is also very helpful (safe the damn tech one) since purge cost a lot less than any heals, gives a small healing with Sith Purity, and will counteract damage to your shield, or at the very least, save you a dark infusion.
I'm currently level 38, and since DK, I have not seen a champion that really scared me in open world. They do take a long time to get down tough.