i know how you feel. i go through that almost weekly. (i am transitioning)
i don't like short hair on me either. so i am transitioning.
here is my two cents:
1. you have been natural for 5 minutes. so it is a little too soon to quit imo. you don't really know what you are doing yet.
2. if you texlax now your hair will still be short. so texlaxing or relaxing will not solve your problem. it may however give you another one....feeling like you quit too soon.
3. hide your hair. anytime in my whole life that i have had to cut my hair due to damage, i hid it away for months at a time. this way i could still feel ok about my hair AND take care of it and maximize my retention. i would wear a wig, a weave, a bun (i know your hair is too short to bun. just saying that's what i used to do) maybe braids or a weave can be an option if you get someone who won't braid your hair too tight and damage it.
4. go on you tube and try to learn from other naturals. specifically look at people who have been on awhile so you can see them grow from TWA to longer lengths.
5. give yourself a better timeline than 3 months. lets say you pick a time period where you can actually see some length, like a year...... or 6 months at least. if you are still unhappy, texlax. ain't nothing wrong with that. also, if you texlax and decide to transition again, it will be easier.
there are plenty of naturals that started out not knowing how to retain length. it takes time and patience to learn your hair. no matter what style you choose.
in the end, do what will make you happy. don't be pressured by
yourself or others to do anything you don't want to do. it is only hair. it will grow back as long as you don't do something crazy to it....most choices are reversible. some just take longer than other.