Generally aloe is used fresh. The leaf is cut open and the juice just smeared on the injury.
For an infection though I would recommend grinding oatmeal and thyme (Thymus vulgares), and plantain (Plantago major) or Lavender (Lavendula officinalis, angustifolia) if you have it, finely and mixing it with honey to make a thick paste. Then you would put a thick coat on the infected area and cover with a bandage. The honey and oatmeal will draw the infection out and help heal, the others (and honey too) will help kill the bacteria that is causing the infection and also aid in healing the wound. If all you have is just oatmeal and honey (or one or the other) just use that. If you only have oatmeal you will need to dampen it slightly before you apply it.
Aloe is not normally made into a tincture. To make a tincture you fill a jar with herbs and then pour vodka (or a different spirit, you can use pure alcohol like everclear but you will need to dilute it as the water pull some properties out that the alcohol doesn't) over the herbs until the jar is full. Set in a warm, dark place and shake 1-2 times daily for 2 weeks. Then strain (you may need to strain a couple times to make sure all the particles of the herb(s) are out), pour into a sterile bottle (preferably dark colored) and label and date. You may need to add more spirits as the herbs absorb it. You can also substitute vinegar or glycerine for the alcohol but that does reduce the potency because they don't pull out as many of the herb's properties as the alcohol does. Store in a cool dark place. If done correctly the alcohol tincture will last infinitely, vinegars can last a few years and glycerine tinctures slightly less.