Jessie,
Now, I am not a trainer, so I'm just going to answer this based on my own experience. I DO NOT think you are a wuss!!!! If you are just starting to exercise it is not at all surprising that 3.5 feels too fast for you. Don't feel pressured by your sister or anyone else. Only YOU can tell what feels right. If it hurts (really painful, not just exercise burn) or you feel like you are going to fly off then SLOW DOWN! At first I was going to say slow down if you are uncomfortable, but exercise is not really supposed to be comfortable, so forget that!

Later you will be stronger and able to push yourself harder. For now, I think it would be best to go at a slower pace and then build up to going faster. I have been exercising for years, sometimes very regularly and sometimes not. I just recently started running (I'm heavy - need to lose at least another 100 lbs) so now I am going 4.5 to 5.0 mph. When I was not pushing myself to run and was just walking, I went at 3.0 for a warmup and then 3.5 was the bulk of my workout. Sometimes I would push it to 4.0 at the urging of my trainer friend. But that was only after exercising for a while. I also think your height makes a difference. I am very short (5'2") so 4.0 is a jog for me, while it may not be for someone with longer legs.
The other thing that I found about going 4.0 was that at first I tried to walk fast at that speed. I felt crazy awkward, uncomfortable, etc. When I switched to jogging at that same speed it was MUCH easier! I know that does not make much sense but there it is. Just try different speeds, walking, jogging, and find what feels right to you.
Your workout is not supposed to be a "walk in the park" so once you get more comfortable on the treadmill, say after a few days or so, you should try to push yourself. You want to be working up to a good sweat. You may also want to keep working on those intervals you tried. You will be shocked to find out how quickly you will build up your endurance. I was NEVER a runner and NEVER thought I would be but three weeks ago I started the Couch to 5k program (you can find it at www.coolrunning.com) and I am so PSYCHED!!! Pushing myself physically is the best thing I've ever done I think. I'm planning on running a 5k in June!!!
Anway, keep up the good work and remember to listen to your own body, not your sister. If you ever get a trainer (which I would recommend) than definately listen to her/him. Your trainer will push you beyond what you thought you could ever do - at least she should! If it wasn't for my 2 friends who have been my trainers I never would have pushed myself as far as I have.
Good luck!!!
Heather