I wouldn't be too worried at this stage of the game... and you shouldn't be under any "pressure" to solo. Why do you feel under pressure?!
I know it's always easier said than done, but try to relax more, and don't get too hung up on what happened on the last flight. You seem to be remembering any negative parts of a lesson, but think of the positives... you handle the aircraft fine, perhaps you have a natural flair for the handling aspect? I'm sure a lot of things are going right, so don't worry about the couple of bits that weren't too good.
It sounds like you have a good mindset and are keen and determined to do well. Every pilot can ALWAYS do better, even if it's only a small issue in their own minds, and they feel they have let themselves down. Don't beat yourself up about it. Some of the best people feel this way, and continually strive to improve. The ones to watch are the people who think it's all a piece of cake (almost said a naughty word!) and they have no trouble with anything, as it's all so easy for them. It's mostly the cocky ones who have the accidents, not the conscientious people who continually want to improve. I'm sure you're not one of the cocky types, as if you were, you would have come on here saying you're perfect, and your instructor has it all wrong. (It's happened before!)
When you're ready to solo, your instructor will send you. The decision lies with them. There shouldn't be any pressure to do it in a minimum time, or any nonsense like that. You're not trying to pass Top Gun, or an ETPS course, so don't talk silly about "making the grade", as there isn't really a grade to make! In the big scheme of things, a PPL is a very basic qualification, and without wanting to rubbish any proud PPL holders, it's not such a difficult thing to achieve. The real learning, and improvement of techniques/skills come with time, months, years, even decades after you did your first solo, and got your PPL. During this time, you'll see that even the pro's get things wrong, and mess things up occasionally. That is how you build experience, and everyone makes mistakes, however minor, and none life-threatening they may be.
Ideally, you should discuss the things you have mentioned on here with your flight-school/instructor and this should help matters.
I don't know you... but as far as continue/don't continue; if you have the money you should continue (within reason). And don't lose any sleep over forgetting to turn the DME on! Do you even know what DME is, at your stage of the game?! The carb-heat can stay on all the way from the downwind checks to final, and be returned to cold at 300 or so feet (in case you need to go-around). I'm not saying do that, just that I've seen it done that way, and there's nothing wrong in doing that. Maybe your instructor wants you to return it to cold 10 seconds after you turned it on for your downwind checks, then use it when necessary as you reduce power again afterwards. There are reasons for both ways. Some people say ice is unlikely to form at power setting less than 2100rpm, so if you're flying a large circuit, belting along at cruise power, you don't need carb-heat. On the other hand, for a smaller/tighter circuit, you leave the carb-heat hot from the downwind checks, as you'll start descending (bringing the power back) straight after. Ask him/her what they want to see, make sure they explain why they want you to do those things (relevant to that aircraft/engine/circuit), and ensure you fully understand what they are looking for.
And another tip... Once you've started up, and come to turning the radios on (following the checklist, which I hope you are using), make sure they are all on before you even think about tuning anything or taxying. That way, in future, when you start flying things with more radios/GPS type equipment, everything is up and running, and initialising (warming up) etc from the start, and you're not faffing about trying to fire-up a GPS as you cross the hold to takeoff and head "direct to" a GPS waypoint (there's that experience thing again!).
Have fun, enjoy it (we all have "bad" days), and continue! Just try to have a positive attitude, stay calm and things will come together with practice. I don't think you've let yourself down, if, in your mind you didn't achieve 100% in a lesson (because you're too harsh on yourself.) The only way you would be letting yourself down, would be by not continuing towards getting your PPL! So stick with it, and continue to enjoy, and learn all you can about the wonderful thing that is piloting.