Yes, it's the right stuff. How much does he weigh. If he weighs a lot, you might want to get the Tylan 200 instead. Another option is Baytril. That might be cheaper, and you don't have to give as much.
Sorry your goose is sick. I would give it orally no less than twice a day. Tylan injections can cause severe injection site reactions.
Dosing options.
0.25 ml per pound of body weight orally four times a day
0.33 ml per pound of body weight orally three times a day
0.5 ml per pound of body...