Worried that you may get genital warts? Doesn't seem like it is worth the cost. Wait until they do show up, if ever. However, you should assume that you have what he has (not had since the virus is forever). Not everyone who has the low risk strains of the virus gets warts. About 50% of the sexually active adults who have the low risk HPV literally have no symptoms (no warts). Which is why so many have this virus.
Thank you! Not so much worried about getting genital warts but more about, do I have HPV and a chance developing cervical cancer, since I hear that is a possibility. Also worried if he and I split up, do I need to let my next partner know.
The low risk strains do not produce cervical cancer. However you should get tested every few years to make sure that no pre-cancerous cells exist. Feel fortunate that you can be tested!
Should you and your BF split up, then what you divulge to your next partner is up to you. Most doctors do not recommend saying anything to future or current partners because most sexually active adults have it anyway. More importantly, you have not been diagnosed with it and so what will you say "I may have HPV because an exBF had it"? You may not have it too. Not everyone who sleeps with someone who has it gets in. The medical community doesn't know why.
It is a personal choice and if you do say anything, but do it in front of a computer so your future partner can see how common it is. Educate your future partner, so they understand the odds that they have already been exposed. http://www.cdc.gov/std/hpv/stdfact-hpv.htm
It also comes down to whom you sleep with in the future. Is it some guy who has slept with every girl that walks in front of him and has had a lot of unsafe sex? Then he probably has it and it isn't worth telling him. If he is someone who has always used a condom and has slept with less than 4 women, then it may be worth it. To educate him, at least.
I really appreciate your time, words and clarity. Thank you!