You said you had a therapist appointment last Thursday. Did you discuss with him? This is not something you want to have go on, so you need to talk to a professional asap so they can make a decision whether or not you should switch meds.
Suicidal ideation can be a side effect as you know and it is dangerous. I'm glad to hear you do not want or plan to act on it but you need to call your doctor today/tomorrow and tell him about the thoughts. They will guide you best and it's important that you do this! Let us know how you are doing!
Can you explain for us so we can better help what you mean, you just found out you have anxiety? Also, how old are you, how bad is your life affected so far, are you seeing a psychiatrist or a regular doc, and did anyone recommend you try therapy with a psychologist before you went on medication? As mentioned above, this is a common side effect of taking brains that affect brain neurotransmitters -- even with drugs that, say, help people stop smoking. It's more common with young people than older people, though it can happen with adults as well. This is one reason why with younger people medication is usually used only if therapy doesn't work and life is severely affected. So again, how old are you and what else did you try before turning to meds?