Well... I play trumpet and i love it, but my 15 year-old cousin wants me to play bassoon. What should I do?

At least give the bassoon a fitting trial period! A few months would be good. hopefully with some instruction from a teacher. Then hopefully you'll be hooked, or at least you'll have a better idea of what you want to do. Definately give it a shot!

Bassoon and trumpets are both very nice instruments (when played well)-listen to bassoon recordings, and if you find a shop that sells bassoons they might let you try one

However some people have said you can't play lip reed and double reed instruments at the same time, so perhaps post on a brass forum too and see who plays both.

Don't take up the bassoon just because your cousin tells you to. Play whatever you want to play, otherwise playing will become a chore and you wont want to do it anymore. If you love the trumpet and you're not interested in playing the bassoon then don't. If you're interested, go for it. If you're interested but don't wanna give up the trumpet, then have a word with your teacher. You might not be able to play bassoon until your trumpet embouchure is fully mature (which will take a long time), and you're teacher will have a much better idea about that. I don't think there are many bassoonists that play trumpet too. If it is a problem, then think about which one you'd rather play.
I'm all for more people playing the bassoon, but even so, i repeat: DO NOT play bassoon just because your cousin tells you to.

Like said above, don't switch because someone wants you too. If you really do like bassoon, don't worry, it's not that hard of a switch. I do in fact play both baritone (when needed, usually for pep-band) and bassoon, so I can say this from experience. It is a little difficult at first, but you'll catch on quick enough (that is, if you decide to make the switch). In the end, do what you think is best.

If you do enjoy the bassoon because you like playing it and listening to it, then go ahead with it. I play trombone and bassoon with no embouchure problems as does one of the Wyoming all state bassoonists and one of my past teachers. Here in Wyoming there seems to be a thing with people playing bassoon and trombone. If you like both and give each instrument its needed practice time then you should be fine.

Ruth88 speaks the truth. That's exactly what happened to me. I played trumpet because my cousin did... and really I don't like playing it that much.

Bassoon doesn't seem to effect my trumpet playing abilities.