As Gaser suggests and attached file,TGA will give you an answer.

Surface Enahanced Raman Scattering, SERS may also be suitable to find out how much amoxicillin is bound to your gold nanoparticles. This could be use Together with TGA, as SERS is dependent on size / shape concentration of your gold particles, which may change between batches or be dependent on amount of amoxicillin. I'd add in a SERS standard to make the measurements relative to each other: the SERS standard may be silica encapsulated dye loaded gold particles to ensure no interaction with your sample. Or add a nitrile or alkyne as an internal standard: see previous answer for more info:

https://nanoscalereslett.springeropen.com/articles/10.1186/1556-276X-8-47

https://www.researchgate.net/post/What_would_be_the_best_resonance_label_eg_triple_CC_bond_yn_containing_to_give_the_most_intensive_SERRS_signal_for_532_or_785_nm_excitation

You can take the comparable FT-IR spectra of gold np and attached antibiotic gold np, which completely give the information about the different pattern of functional group in IR spectra and further you can compare by TGA analysis.