I would use Neosporin on the tick bites but you'll need something different for poison ivy. There is a product called : Ivarest that works really good. It can be found at most drug stores like Walgreens or CVC or Rite-Aid. Then there is always the good old stand-by Calamine. Messy but does the job!
Visit your pharmacist and ask him/her for something called shake lotion. It's great for poison ivy. If they don't have it, calamine lotion and a little menthol go a long way to alleviate itching.
Neosporin & Ivarest are both antibiotic. Both work for tick bites and found in www.amazon.com