I used my Philippine passport to book an airline ticket, but I'm also an American citizen. Will this create problems with immigration?
You should use your US passport on your flight registration, and to check in. This will ensure that US Customs and Border Protection realizes that you are a US citizen and, of course, that no special authorization is required for your admission.
Other posters will state that as a US citizen, you have a right of entry, and of course, this is true, but if there is any doubt about your citizenship when you present yourself, you may endure delays while your citizenship is established. Also, the airline may refuse to carry you if it has any doubt of your US citizenship, so you may not have the opportunity to plead your case in the United States. A US passport categorically proves your US citizenship. (Note that a birth certificate by itself does not; some US citizens do give up their citizenship voluntarily, for example, to avoid having to continue making US tax filings after becoming expatriates.)
Get a US passport, if you don't already have one. If time precludes you from getting one, and you have a recently expired one, bring that as your evidence. But I strongly encourage you to use a current US passport to enter the US each and every time you do so. (A few other current valid methods can be used when crossing the land border, but they aren't relevant to this question.)
Can I return to America if I used my Philippine passport although I am an American citizen?
Will this create problems with immigration?
The US Supreme Court had decided in 1967 that US citizens cannot be deprived of their US citizenship against their will. The case is Afroyim v. Rusk:
... the [14th] Amendment can most reasonably be read as defining a citizenship which a citizen keeps unless he voluntarily relinquishes it. Once acquired, this Fourteenth Amendment citizenship was not to be shifted, canceled, or diluted at the will of the Federal Government, the States, or any other governmental unit.
In addition, a central right of US citizenship is a right to return to the United States. If you are a US citizen, immigration officers cannot refuse entry.
However, I answered "probably not" because I have heard a few stories of people being challenged by US immigration officers on the basis of their dual citizenship. My sister, for example, was once told by a US immigration officer that it is "unconstitutional" for her to have a passport of another country.
I have also read online of people being told at the land border with Canada that they need to renounce their US citizenship if they hold another passport. Such officers are not acting according to government policy. If any officer of the US government says anything like this to you, you should refuse to comply.