Please help me figure out the problem w/ my car

2000 Oldsmobile Intrigue with 147,000 miles with a v-6 engine. When trying to crank the car up it takes a minute as if it isn't catching it makes an iiiiinnnnnttt sound then it starts up. Then when you put the car in drive it hesitates on whether to turn off or go. So one night while I was out at the gas station the car wouldn't go into gear, I'd put it in drive it would reave up but it wouldnt go anywhere then I tried it in reverse the same thing happened. The next day it acted perfectly fine my uncle came out and put a new air filter on it because the air filter had never been changed, so the problem had seized so then when I proceeded to take my sister to alabama for school it cut off and on all the way back home. Is that because I need a new transmission or do I just need work done to the car itself because someone told me it was the transmission?