Yes and no. Applying for credit creates a inquiry on your credit report. An inquiry is used to determine risk. For example, someone with no credit applies for 2-4 credit cards wont raise red flags, but someone with existing credit (good credit) applies for 4-6 credit cards, it will hurt their score. This is all based on risk. People applying for alot of cards have either their credit stolen or they are desperate. The sad fact is, people will apply for alot of credit, get the credit and run that up right before filing bankruptcy. A few inquries will hurt you in the short term, but they are dropped off completely in 2 years and are usually disregarded in 1 year.
Another important thing to check is who you are applying with. If you apply for two chase cards in 6 months, you will be denied.
This is due to a "Cool down" period. It prevents excess risk by limiting new accounts to consumers to one for every 6 months(ive confirmed this with chase). And this is regardless of your credit. But the problem is, you may be approved for one chase card, but every other chase card you apply for will increase the number of inquries (although you are denied anyways due to it being within the 6 month period. From my understanding, this is the way the system is setup, not intentional).

There is a site called CreditKarma that will allow you to pull a score (for free, no subscription fees, no gimicks). It will give you a breakdown of what is hurting your credit and a score (which is not FICO). This is a "Soft Pull" and will not hurt your credit.