Welcome to the fold! Don't worry about having to go two sessions at first, you're still getting most of the benefit. And it won't be long until you're easily going 20 minutes at a time.
And you're also right about trying different kinds of oils. As for your sesame oil, if you're using toasted, you will feel like gagging and you won't get the benefit you would from unrefined, untoasted.
Even so, sesame seed oil never agreed with me. My two favorite oils are flax seed and coconut (again unrefined, virgin, etc). Part of the fun is trying the different oils to see how they affect you.
Coconut is one of the best for oral health because it whitens teeth, roots them more firmly in your gums, and kills bad bacteria that can be in the gums or even in the root canals.
One odd thing about coconut oil for me is that is REALLY helps me sleep. I could take Nyquill, Melatonin, and all kinds of sleep aids and NEVER be able to sleep in past 6am - and feeling miserable when I wake. If I use coconut oil before bed, I'll sleep like a baby until noon if nobody wakes me.
The other oils keep me awake all night (which is one reason its advised to do in the morning). Weird - but part of the fun of experimenting.