What are some excuses to not go swimming?

You can say you caught cold these days, it is not suitable for swimming, the doctor said to pay attention to have a rest, don't touch cold water, in order to avoid serious condition

Say: you the previous time you went swimming you got an ear infection, and you don't want to get one again.

You can say you get swimmers ear really bad. My cousin gets it almost every time we go swimming.

Say I don't want to go cause my mother said so. Don't lie, you'll grow up with a bad habit.

Before you leave go to the toilet and puke or pretend to then make sure you parents or whoever is taking you knows that you have puked so then you won't have to go also act really weary when walking so they can notice that you aren't strong enough to swim that usually works for me

I suggest talking to your mom and tell her you will look like a baby staying in the shallow end of the pool which would be very embarrassing. Tell her I will look afraid of the deep water and/or that I can't swim and neither of those things is true. Tell her you don't want to go on the field trip if she is not going to let you fully participate in the activities.