As someone who has done a bit of brewing, id back up what has been said earlier in that you should ditch the milk jug. If you can find something glass at that size, that would be best, failing that you can buy sterilizing products from brewers shops, there are a few homebrew ways to make sterilizers cheaply, though if you use any sort of chems to sterilize, you need to clean your flask out over and over and over and over (seriously like 6 times) with clean water (fresh each clean) to remove any traces, as sterilizers will kill your yeast.
If you can get glass, a great way to sterilize is capping the top with foil (use a bit about as big as your palm for something about beer bottle size, bigger for a bigger hole) just place it on top then smooth the sides down with your hands. Then place your bottle into an oven. THEN turn the oven on to about 150 C. Turning the oven on after it goes in will let the bottle heat up slow and then there is no chance of cracking. Cook it for about 45 mins-1 hour, If there is any glue/labels on it it may get a bit of a burning paper smell, dont stress. Then turn the oven off and just let it cool. This is basically how alot of labs sterilize glassware, once its done, if you leave the foil on it should stay sterile for a fair while, (eg, months) and will kill bugs better than sterilizing powders, is nearly free and doesnt require large amounts of flushing with clean water. Metal lids can be boiled to sterilize as well.
Other thing that can kill yeast fairly quick is water with chlorine in it, even many bottled waters will contain chlorine. An easy and cheap way to be sure to clean in out in your own kitchen is to fill a big pot with water and bring it to the boil, then uncover and leave to boil, the chlorine is one of the first things to come off when it boils. Boil it for about 10 mins uncovered, then remove the heat and let it cool enough its not going to kill the yeast. THEN add your yeast
I make beer from homebrew kits on a regular basis and I boil all my water like this and while it is still fairly hot I put it into the sterile keg with all the sugar, etc. Once I have enough water I seal the thing up and leave it till the next day, then crack it one more time to put the yeast in.
Simple way to make an airlock (ive tried the balloon without great success) is attach a rubber hose to the lid of you jug, then drop the end of the hose into a bowl of water, bubbles of gas come out, nothing comes in