Just to add to Mr. Colleluri's correct response. The civil litigation department at my firm has handled numerous bed bug cases all to a successful conclusion. In NY, over 100 bites on one person alone would get a significant settlement if the claim can be proved. Many times hotels claim that the guest brought the bed bugs into the hotel. You will also want to check your luggage to make sure that none of the bed bugs made their way into your luggage and were brought home.
We cannot represent you as your case would be based in California and I am not admitted in that state. But in researching this issue over the last two years, we have found that almost all states have bed bug issues . You can look up the hotel you stayed at on bedbugregistry.com (I have attached a link below) to see if they have ever had this problem before. If not, you may want to post your story on the site. I also suggest you "Google" "bed bug bites in San Diego, you will get quite a few news stories about prior cases where the lawyers names are mentioned. That might be a lead to find qualified counsel. Good Luck and I am sorry for the miserable experience you had to go through.
Yes you can sue and it is a growing area of personal injury law. With over 100 bites you should have little problem finding a lawyer who might be interested. Get all your documentation together, take pictures of the bites and have her seen by her pediatrician right away.