Difference between shall and should

[Juan Jimenez]

Test No. incompl/elem-17 "White Water Rafting", question 5

Are you really suggesting that we ......... actually get into one of those ridiculous things?

(a) shall
(b) will
(c) should

Test No. incompl/elem-17 "White Water Rafting", answer 5

Are you really suggesting that we should actually get into one of those ridiculous things?

Correct answer: (c) should
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Hello I'm not sure about the difference between shall and should in question

[Mosteque]

Shall may be used with first pl and singular person: We shall see, I shall do this
When sb suggests you sth, he/she suggests that you SHOULD do sth.
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obsequium amicos, veritas odium parit

[itsme!]

So whats the difference between this two sentences:

I shall go to the doctor
I should go to the doctor

thanks