2004 Citroen C3 Limp home mode

I think I have an oil sensor problem. For starters, every time I start my car it says I have no oil (even though I do) but this is not my main problem. After about a minute or so of driving (usually when I accelerate to make it up a hill) the car makes a huge jolt or jump if you like as the sport and snow lights flash away in unison while beeping 3 times to indicate an issue. After this jolt, the revs run slightly higher then normal but wont go over 2000rpms. This is very frustrating in traffic because my car will now take AGES to pick up speed. The strange thing is that this will only happen when my car is cooled. As soon as my temperature reader/indicator shows my my car has been warmed up, I stop and restart the car and then I have no issues. But if I try restart BEFORE the car has warmed up, it will do the same thing again.
I have done a little bit of google-ing on this and it does appear to be a common issue. I've seen it referred to 'limp home mode' but no one seems to offer a solution. I've read about plenty of people spending hundreds or more trying to solve the issue but failing. I don't want to be one of these people.
I've taken it to get a diag and the guy said there were 13 faults which he apparently fixed but I have seen no improvement. He said he also 'reset' my car computer. My mechanic told me he wants to clean out the oil filter and sensor first and if that doesn't help then replace it.
Ive has this issue ever since I bought the car second hand about a year ago so it's probably had this issue for a lot longer than that.
To date, I have spent about $700AU trying to fix this. I would rather not spend any more if there is no solution. I had the fuel pump replaced, the diag/repair and a general service / look over.

Please help me!

Thanks, Taylor