Can I be considered myself as full time student even though I only started school from September 2023?

It depends on why you want to be considered a full time student (FTS).  For some tax purposes, you must have been a FTS for parts of 5 calendar months. Sept. to Dec. is only 4 months. If you were you a high school (HS) student earlier in the year, that counts as being an FTS.

To be eligible for a tuition credit, you only need to be a half time or more student and not for any specific period of time.

If you are in the personal info section, of TurboTax (TT) answer no to the FTS question, if you were not in HS earlier.  If you were over 18 on 12-31-23,  not being a FTS may make it more difficult for your parents to claim you as a dependent.