Can you just cut out gluten...yep, you totally can. Celiac or not, if gluten causes you trouble then removing gluten is your solution. Easy.
However, if you wish (for whatever reason) to have a firm diagnosis of Celiac then you must continue with a gluten full diet and seek additional testing. A GI doc should run a full Celiac panel (blood work) if your PCP didn't (some PCPs run 1 basic test but not the full panel). A GI will also likely want to do an endoscopy. It's possible to be a sero-negative celiac (neg blood tests) and have a positive endoscopy. Once you remove gluten from your diet you immediately begin to reverse any damage/inflammation. So your testing will be false negative.
Now, all that said, I'm sero-negative and my PCP didn't think it necessary to refer me to a GI so I didn't have any additional testing or endoscopy. I could be a celiac or I could be non-celiac gluten sensitive (which is my PCPs official diagnosis). The treatment is the same...no gluten. It took me probably 4+mos gluten free before I really saw improvement but once I hit that benchmark I never went back. I didn't need a Celiac diagnosis to make me commit to GF nor did I need it to convince my husband/family of my need to be GF. However, I know some people who feel they can eat a little bit of gluten and still feel fine. That's fine and all but if you are truly celiac, eating gluten causes intestinal damage that can shorten your life. I pretend I'm a celiac cause it's possible I am. I'll treat my body as if I am just to be safe.
I hope that helps.
If you wish, feel free to PM me info about what blood tests your doc ran and what the results were. Some docs are really REALLY inept at celiac testing and I've know a few people be told they are sero-negative only to learn the doc misread the results or didn't test the right thing.
Mom to two amazing DDs ('07 & '09) and a fur baby.
Gluten free since Nov '11 after non-celiac gluten sensitive diagnosis. Have had great improvement or total elimination of: migraines, bloating/distention, heartburn, cystic acne, canker sores, bleeding gums, eczema on elbows, dry skin and scalp, muscle cramps, PMS, hair loss, heart palpitations, fatigue. I'm amazed.