Hi! I'm Mia! Please find my corrections below. I don't really use the word, "swamped" unless I'm talking about work, often in, "I am swamped with work". I just use it when I pertain to being overloaded with work.

I'm not saying the use of the word "swamped" is limited to this sentence. You may ask other tutors for their thoughts on this. =)

I'm swamped with~

1. I'm swamped with homework. - OK

2. I'm swamped wiht the new job. - I'm swamped with work in the new job.

3. I was swamped with the work when you called me yesterday. - I was swamped with work when you called me yesterday.

4. I'll be swamped with the new job for a while. -I'll be swamped with work for a while because I just got the job or because I just started.

5. I'm swamped with low salary. - I wouldn't use "swamped" here. I would rather say:

The salary sucks. - informal

The salary is disappointing.

6. I'm swamped with my test on Sunday. - Did this event happen in the past? Are you trying to say that you are busy taking that test?

I would rather say:

I was taking my test last Sunday. - past

I will be preoccupied with a test on Sunday. - future

I am taking a test. I'll talk to you later. present

7. I swamped with the English test last year.  - Do you mean you the English test kicked your a**/ was a big challenge last year. Pardon the options I've written down. They are really effective expressions. If that's the case, then I would say:

The English test kicked my a** last year.

The English test was a big challenge last year.

8. I'm swamped with the noisy childeren. - I'm irritated by noisy children. or Noisy children annoy me.

9. I'm swamped with the new project these days. - OK

10. I'll be swamped with bills. - OK

Cheers,

Mia