Is emission of semen the only sign of puberty?

Puberty has signs which are well known for both males and females. For a male, puberty is reached when one of three things happens: the emission of semen, the growth of coarse hair around the private part, or reaching the age of fifteen. 

For a female, puberty is reached when of these three things happens, and there is a fourth sign, namely menstruation. 

It is not essential that all of these signs appear, rather one sign is sufficient to establish that a person has reached puberty. 

See: al-Sharh al-Mumti’, 6/202. 

The fact that you have reached the age of sixteen indicates that you have reached puberty, even if no semen has been emitted. 

You should note that you are now mukallaf (accountable) and are responsible for your words and actions, as the Prophet (peace and blessings of Allaah be upon him) said: “The Pen has been lifted from three: from a child until he reaches puberty, from one who is asleep until he wakes up, and from the insane person until he comes to his senses.” Narrated by Abu Dawood, 4402; al-Nasaa’i, 3432; al-Tirmidhi, 1423; Ibn Maajah, 2041. classed as saheeh by al-Albaani in Saheeh Abi Dawood. 

We asked a doctor about your situation and he said that it may be the matter of sickness, or it may be something natural, so you should refer to a specialist doctor to find out what is going on. 

We ask Allaah to guide us and you. 

And Allaah knows best.