IF, you are having chest pains, then you should 1st go to the ER. After an ER visit, then most ER's will suggest you make an appointment with a cardiologist for a follow up appointment.
No, with straight Medicare, you don't need a referral from your primary doctor, but in most cases, if a (new) patient, then they will want your medical records from your GP (prior) to your visit, thus after, they would forward your records to your GP.
And with (any) specialists, (new/current) to get an appointment usually is difficult and many times, can take weeks/months to get the appointment.
I went to the ER in December for kidney stones and was told to have a follow up with a urologist w/in a few days, but my 1st appointment was not for almost 3 weeks to get in.
Now, what if your complaints are not what you think they are, thus do like most of us and google them, only to find out that what you suspect is not what is wrong with you. Now with many GP's, can get into their offices if needed w/in a day or 2, and after the GP examines you and if they (believe) you need a specialist, then most offices will schedule you while there at the office and usually will save time.