A lot will depend on the particular product your are using, and what active ingredient it contains. Read the instructions for the specific product and follow them. This sounds elementary, but it really matters.
For example, one thing that stood out to me in your post is that you mention applying the product to your skin directly. If you are using a DEET- or picardin-based product that may help, but if you are using a permethrin-based tick repellent spray product, this could be basically useless because the permethrin products are typically designed to be sprayed on your clothing, not your skin, and will break down quickly if applied to skin (think like 15 minutes) and then not do anything. If, however, you spray the same product over your shoes/socks and lower portion of your pant legs, you might be over 70x less likely to be bitten by a tick (
https://www.nytimes.com/wirecutter/blog/permethrin-protect-from-ticks/). Ticks most often get on you from ground or grass-level and crawl up your body, rather than falling on to you and working their way down, so protecting your feet and legs by wearing long pants tucked into socks is a solid strategy, whether or not you add a chemical repellent on top.
For the Sawyer line of tick-repellent products, for example, the company notes "The warning labels on the cans or bottles are often misunderstood. Your skin metabolizes, or breaks down, Permethrin within fifteen minutes of contact with skin. Therefore, it is of no value to you as a personal protection insect repellent when applied to the skin. In addition, the EPA precautionary statement, “Do Not Apply to Skin” indicates that Permethrin is ineffective when applied to skin; therefore, do not apply to skin." Again, read the directions for your particular product.
Also, the same product might offer differing levels of protection for different target pests. I'm seen claims, for example, for certain DEET products that they might help repel mosquitoes for as long as 12 hours, but ticks for only 8 hours.
Once you've been bitten by a tick, applying additional repellent won't help you against that particular tick. If anything, you might do harm by introducing the repellent product into a wound and irritating your skin. You'll need to pull the tick off using tweezers. Try to keep the tick whole as you pull it off rather than crushing it, then save the tick in a small plastic sandwich bag so you can show it later to a doctor or entomologist. Different species of tick can be vectors of different diseases, so showing a professional the tick that bit you can help a professional assess what risks you might have been exposed to.
Here's some links for further reading if you are so inclined:
https://nymag.com/strategist/article/effective-tick-repellents.htmlhttps://magazine.medlineplus.gov/article/understanding-and-preventing-tick-biteshttps://www.consumerreports.org/insect-repellent/how-to-use-permethrin-on-clothing-safely/https://www.epa.gov/pesp/reducing-risk-tick-borne-diseases-through-smart-safe-and-sustainable-pest-controlhttp://npic.orst.edu/pest/tick/index.htmlhttps://www.epa.gov/insect-repellents/find-repellent-right-youhttps://www.cdc.gov/ticks/