How would I know if I was adopted?

Adoptions take a minimum of six months to be finalized - yours was filed too soon to be an amended birth certificate. 

As another person said, the easiest way to get a definite answer is with a DNA kit from ancestry.com, or 23andme.com - the cousin matches will tell you if you have a different original family. 

birth certificate

Probably the most definitive way to find out if you are adopted is to conduct a DNA test. If you have already spoken with your parents and they are not forthcoming, you may ask if a DNA test can be performed.

In the US, an adoption can't be finalized for at least six months. At that point, a new birth certificate is issued showing the names of the adoptive parents. That means that if your birth certificate was issued before you were six months old, you're not adopted.

Now as for why your birth certificate was two months late. Since birth certificates aren't issued at the hospital, it's not unusual for the paperwork to take some time to work its way through the system. Two months doesn't sound abnormal.

Not to put ideas into your head for you to stress about, but occasionally there are situations like the parents using a sperm donor and/or an egg donor. Those things wouldn't affect the birth certificate at all. You could tell your parents how you've always felt like you're different, and ask them if you're adopted. Even though it doesn't sound like you are adopted, the question would open the door for them to explain if there was something unusual about your ancestry

Ask your parents.

We'll just guess where in the world you are then shall we. Why not look up the laws regarding registration of a name or adoption. You know, something useful.

The register date doesn't mean you were adopted. If you were adopted your birth certificate would have your biological mother's name on it. I was born in December and my birth certificate was registered in May the next year. I was not adopted. 

If you're afraid of being lied to, just send away for one of those DNA tests, like 23andMe or AncestryDNA, each of which provide results that list names of actual people living and dead that you're genetically related to. My uncle just found out that he's my grandma's son but not my grandpa's son that way because the people with the closest DNA match to him who has ever had their DNA tested was my mom, who showed up as only a half sibling, and a girl who lived down the street from them growing up and who also showed up as a half-sibling, meaning my grandma and her dad had to have had an affair and that's how my uncle happened.

If you take one of those tests and you were adopted, then you'll know it because the people that show up won't be from your family. At the same time, you'll find out who you really are a blood relative of and will have a means to contact them.