Think I am too much of a wimp for this!

not pathetic at all!  most of us started from nothing!  getting treated for hypothermia in an indoor pool is INCREDIBLY concerning.  you really need to consult with a doctor on this one, i think.  the rest though - is normal.  i've been doing tris for 5 years and only started adding interval sprints to my run training in the past 6 months.  i would normally say you will be fine, it's just a sprint, just take it easy, but not with this hypothermia thing.  there is something wrong that you need to address before you continue training.  don't give up yet, though!

I personally wish they made down swimsuits, so I can relate!  I got hypothermic snorkeling in the Caribbean, and had to wear 2 wetsuits when diving. 

Great suggestions here already- a couple of other thoughts.  Since you can't really swim fast enough to stay warm, at least try to warm up before you swim to get your body heat going- it will be a lot harder to get warm once you are in.   This is also important before you race, but you may want to warm up on land instead of the water.  Definitely get a full wetsuit for the race- a lot of people won't use them in a sprint, but for me it's well worth the few seconds to take it off.  You  might also want to think about getting a neoprene cap (I think they are usually allowed)- you lose a lot of heat through your head.  Neoprene booties may be allowed but sadly I don't think gloves are (my hands get really cold!).  

If race day is warm you should heat up quickly on the bike, but I've raced when it's been cool- in that case you might want to throw a long sleeved top over your trisuit- if you get a belt for your race number you can easily pull it over the shirt.  Arm warmers are also a great invention and a chilly girl's best friend .   

As for non-meat protein greek yogurt and beans are decent sources.  If you are anemic that could worsen your cold tolerance- I agree with seeing your doc. 

Welcome to the sport.

We're nothing special, just silly enough to sign up for a 3-sport race.  

Keep swimming, even if the sessions are short and get some lessons if you haven't so you learn good technique up front.  You can swim any stroke you choose.  Front crawl is most efficient, but also an easy one to get tired doing.  Breastroke and backstroke are acceptable, especially for a pool swim.  (You'll probably see some athletes walking in the shallow end if they can...)

Before you go to the pool, start picturing in your mind what a "good" swim looks like.  Keep that POSITIVE image in your mind the whole way to the pool, in the changing room, in the shower, on the pool deck, and in the water.  Whether you go in excited to swim, or dreading the cold water, reality often aligns with your attitude.  You may not be able to turn up the thermostat at the pool, but you can turn it up in your mind.  

OK

I was a lifeguard and swimming instructor in high school and college (I never swam competitively).  A lot of inexperience swimmers are nervous and tense which makes breathing difficult, especially when they are trying to swim fast enough to "not drown."  They adopt a "blast-and-gasp" breathing style where they exhale forcefully (blast) and gulp in (gasp) as much air as they can in that brief moment when their face is out of the water.  Here are a couple tips that might help when you swim front crawl:

1)  Relax
2)  Slow down (I don't know how fast you are trying to swim, but think of swimming at an effort similar to walking in the park.)
3)  Hum gently while your face is in the water.  It controls your breathing and keeps water out of your nose.  
4)  If you have exhaled with your face in the water, you'll get a quick breath of air when you ROTATE your head to the side.  If you get splashed, put your face back down in the water and blow the water out of your mouth.  Get another breath the next stroke.  If you are relaxed and swimming at an easy pace, you can overcome the loss of one breath.  

When you swim slowly, you'll have to really roll your body side-to-side because there isn't much of a trough next to your face.  As you get faster, you'll find you don't need to rotate quite so far to get air.  (If you watch Olympic swimmers, they have a huge trough and barely roll to breathe.)