16 and possibly pregnant ?

I am a 16 yr old girl and had sex before. I always know to use protection and am aware of the risks but usually dont want to think about them cuz im too scared. Anyways i've held off sex for about a month or 2 months n a hlf, but recently i had unprotected sex 2 days ago(may 26) late at night lyk 1 or 2am. And sadly yes alcohol was involved but i knew what was happening. The next morning(may 27) i had a slight hangover and had 1 before but not where im out and about in dept. stores with my cousin n just felt queasy in my throat n stomach n have headache throughout the day n feeling to vomit. I tried having a bowel movement but it didnt want too go and the 2nd tym i went at night it was lyk liquid :/ and had a hard tym again the next day.

I automatically assume its from a hangover but the next day(may 28) i felt the same sore, and queasy in the stomach n throat lyk cramps but lasted the whole day also the feeling of vomitting and tired n i am driving the whole day. Im no expert but hangovers dont last that long and i didnt drink a whole lot. Also its not my period bcuz i just ended about last tues or wed (may 22 or 23). I spoke to my 'friend' and he said he did not climax in me, but you never can be to sure right?

I looked up online health clinics and family planning places near me and i'm wondering what do i do when i go? What do i tell them? Which doctor or whatever to go to? What do i pay? I am old enough to be alone bcuz it says 15 and up, hopefully thats correct. I'm going to try and go tomorrow (may 29) bcuz you  have atleast 3 days before pregnancy happens, is that true? I've never had birth control, never had a home test n always used condoms except for the first time i had sex who also said he did not climax inside.

So is it too late for me to take birth control cuz tomorrow is my 3rd day? Or is this possible that i might be pregnant when i first lost my virginity without protection which was in January this year but probably not bcuz thats already 5 months n i did not 'grow' or be pregnant from this past weekend? I am very scared and praying that its not happening, and i cant go with any1 cuz i think my mom knows i'm sexually active but maybe doesnt want to believe it yet but pretty soon im being pushed to the point where i have no choice but to openly talk to her. My closest cousin has to work and my close friends are away over summer. I just want to know anything and everything please! Hopefully i didnt leave anything out but if i remember i'll comment or whatever. No negativity please just help...

I know this was a lot i wrote but the more info i write the more you can try n help right, and nobodys perfect and just shows im 0nLy^hUmaN