Frowns I am embarrassed and flattered at your recommendation but will do my best with delicious's question.
Dr Sam Bunting would not be impressed with oil cleansing. She would be banning you from putting any oil on your skin at all!
Have a look at her acne videos with CH on youtube.
Her recommendations would be along the lines of:
Single cleanse with Cetaphil, LRP Physiological Cleanser or Avene Extremely Gentle Cleanser (I love the Cetaphil but have just started with the LRP and probably love it more)
Acid tone with something containing Salicylic Acid - Effaclar Duo is perfect. I liked this and also liked Paula's Choice 2% BHA (probably liked the latter more as it was much cheaper)
Leave off any serums for the time being.
Only moisturise if you think you need it and then use an oil-free product. Personally I found both the Effaclar and Paula's Choice lotion pretty moisturising.
See what your skin is like from doing these 2 steps alone - you should notice an improvement. You may initially get some of your lumps turn into spots or random spots come up in odd places but keep going.
If this doesn't get rid of everything then add in benzoyl peroxide - she has recommendations on the video.
Then when you aren't pregnant anymore (congratulations!) add in a retinol such as LRP Redermic or Avene Ystheal.
And if having done all that the spots aren't gone, see your GP, you need a prescription.
Personally I found a massive improvement in the spots with Cetaphil, a further massive improvement with the Paula's Choice (I bought this before I tried the Effaclar) and a final disappearance of the spots when I added a retinol. Once I'd done all of that my skin also didn't mind oil so much and I do occasionally use oily products but I avoided like the plague to start with. When your skin is happy and spot free, then you can start enjoying playing around with serums. At the moment you need to avoid anything that could make the problem worse and keep to a minimum of products.
For an SPF I'd go for Sunsense Daily Face oil-free as a) it's oil free (can you see I'm obsessed) and b) it has niacinamide which is another nice anti-acne ingredient.
For individual spots I love love love Vichy Hyaluspot which has lots of salicylic to get rid of the spot but also lots of hyaluronic so as they go you don't get that dried up peely skin which makes them look so much worse.