turtle isnt very active at all, what should i do?

ok so i've only had this turtle for 2 days, but im already worried. its hasnt eaten yet and it looks like it just sleeping on the basking area and literally never really moves unless i pick it up or something :(. its a yellow belly slider and i think its still only a baby seen as its still rather small. i thought it might have been hibernating at first, but im sure baby turtles dont hibernate? another thing is that it seems to be quite hard for it to open its eyes, nd i thought this may be a lack of vitamin a, but i cant help it because it wont eat.. i thought about the eye drop stuff.. but does it really work? some say it can overdose :/ and if theres occasionall little bubbles coming from the nose, is that bad? respiratory infection? but i cant take him to a vet at the moment.. what can i do?

sorry for going on and on, i just dont want the turtle to die :'( its my first ever turtle and i would be so upset :(.