That is a great start. It looks like you are using the right antibiotics. However, it is not a sure way of stopping contamination. This sounds like it is probably due to incorrect aseptic technique.
You can increase your antibiotics for the short term until you have multiple cultures, so that you do not lose more time waiting for cells to grow. However, ensure you are using 70% ethanol properly and you are not removing the lids to containers for long periods of time. Lastly, I recommend whenever containers are open, do not move your arm or anything non-sterile over the open lid.
Monitor your cell cultures under the microscope daily, as bacterial contamination will bloom over night. If you see any traces of bacteria change your media immediately. If you catch it early enough you can save your cells. If you are worried your media is contaminated you can filter it with a syringe and 0.22um filter.