Storing, drawing and travelling with an injectable

Storage

Refrigerate at 2 to 8 degrees Celsius. Most products also permit a defined period at room temperature once in use, but that window is product-specific and is on the label. Read yours rather than assuming.
Do not freeze. A product that has frozen is discarded, not thawed. This applies even if it looks normal afterward.
The fridge door is the warmest and most variable spot in the fridge. The back of a middle shelf is better.
Keep it in its original carton. Light protection is part of what the packaging is for.

Once a lyophilised vial is mixed, a different clock starts and it is shorter than the unmixed one.
Bacteriostatic water contains benzyl alcohol as a preservative, which is what allows a vial to be entered more than once. Sterile water contains no preservative and is single-use. They are not interchangeable and the labels look similar.
Label the vial with the date you reconstituted it. You will not remember.

This is where the serious errors happen, and they happen by factors of ten.

Insulin syringes are marked in units, not in milligrams or millilitres. 100 units is 1 mL on a U-100 syringe.
Your dose is prescribed in milligrams. Your vial has a concentration in milligrams per millilitre. You cannot draw correctly without both numbers and the conversion between them.
Work the arithmetic twice, on paper, the first time at any new concentration. If a calculator tells you to draw almost the whole syringe for a small dose, stop and recheck rather than proceeding.
Subcutaneous injection uses short, fine needles. Air bubbles matter less here than people fear, but they displace volume, and displaced volume is a dosing error.

Use a proper sharps container, not a household bottle. Most pharmacies and local authorities operate a disposal route, and it is usually free.

Carry-on, never checked luggage. Hold temperatures are uncontrolled and bags get lost, and a lost bag here is a missed dose plus a replacement cost.
Use an insulated cool pack, and keep the medication from touching ice or a frozen gel pack directly. Freezing it in transit is the common failure.
Bring the original labelled pharmacy packaging. Travelling internationally, bring a letter from your prescriber as well.
Medication and needles are permitted through airport security. Declare them at the checkpoint rather than letting them be found.
Weekly dosing is forgiving about time zones. Keep the same weekday and do not try to correct by hours.