I have a 2009 Honda Civic just got a new battery I jus?

When I start my car it makes these tic sounds and it seems like the battery keeps draining itself so I have to jump start it and it runs, I took it to autozone to check if it had any problems with it and the alternator and checked out fine and everything else I just don't know what the problem can be

Check to battery cables themselves, and if the connections are tight…

See if the battery is being drain when the car is off. Less than 0.05 amps would be good because you have like a clock of whatever still running when off.

Ticking on start up usually refers to hydraulic lifters being bad from bleeding down overnight or sticking because the oil and filter were not changed every 3,000 miles.
All Honda's have a common problem with valves getting tight and the valves need adjusting every 60,000 miles.
If the starter is grinding on the flywheel when you try to start the motor replace the starter.