do you really have to wait for 6 months after card rejection?

Hello,

I applied to Rakuten card on Dec.1st and got rejected.
Miscalculated the date (thought it was 6 months for some reason) and applied to AMEX Gold today and got rejected.

How 厳しい is this 6 month rule? Can I really not apply to any other credit card companies until November?
Sucks because I was planning on having big spendings soon and was going to get all of those sign up bonuses from Amex…