Prairie Fleur, the dose for tylan for an adult bird is 1cc or ml. Don't confuse this with 10th of ml on the gauge which of course will have
a . in front of it. To draw the medicine, pull the plunger back to fill with air before you insert it in the bottle, then depress it putting the air in the bottle. Then follow HEChickens directions. This is a big shot so its a lot of fluid to put in a bird breast. You can make it two shots, but since this is your first time I'd just give it all in one shot. Tylan is kind of a thick medication, so you want a syringe with at least a 22 gauge needle. The smaller the number, the bigger the gauge.
When giving the shot don't try to be gentle. It causes more pain if you don't just insert it all at once. You could practice on an orange with water. That is the closest thing to a chicken breast feel I can think of. Be sure to clean the needle though before you use it on the chicken. LOL
Tylan is pricy but it is the best medication to have around if you have chickens. Have your DH pick up some extra syringes so you have them on hand.
If you don't want to pay the price for Tylan, I have also found that Di-methox which is a really broad spectrum sulfa drug works very well for many things. It can be harder to find though. You just mix it in water according to package directions.
Also keep in mind that if your bird has a virus, an antibiotic will not cure the virus. It will only cure the resulting infections from the virus. So you may not see immediate results and may have to treat a couple of weeks with either shots or medication in water. The virus will run it's course regardless.
I honestly don't like using antibiotics unless they are necessary. You risk creating super bugs and then you won't have any way to cure them later if that happens. I prefer to use probiotics and more natural methods first before giving antibiotics. In your roosters case if you tried the oil to make sure he doesn't have something caught in his throat and he is still acting the same I would use the antibiotics.
Another item to consider having on hand is Oxine. Again you pay for it. But it has so many uses. Be sure to get it with the activation granules which are actually citric acid. You can use it with or without activating it. It is much stronger activated, but for some uses you might not want to. You will have to order that on line. Do a search to find the least expensive price with shipping.
In example, I had a group of chicks in my trailer that started sneezing a week or two ago. I simply put a little oxine (not activated) in their water for several days and it cured whatever they had. I also sprayed down the floor with a disinfectant (you can also use activated oxine and water for that).
I use oxine for all kinds of things. Even mopping the floor, washing eggs for customers, as a foot soak, cleaning the bathroom, etc etc. If it is activated you use so little it lasts for a long long time.
Just a little more food for thought. You can spend a fortune for things for your chickens. But things you buy can also be used for other pets or for personal use. I keep a total pharmacy I think for the birds. I use a lot of the products for my dogs and cats as well. I guess you kind of have to weigh in what is important or not and whether you want to go to the expense. I can say without a doubt that keeping your birds in the best of health is the cheapest way to keep them well. Spending a little more up front saves a lot of expense later on.
Sometimes I get very disgusted with myself because I have so many birds and I have to keep colors and breeds separated. When I had free range birds that mixed I didn't have nearly as many issues with health. The penned birds don't get the grass and bugs and things that they would otherwise. I feel like a bad chicken mom.