I got stuck X(

(See 1) below)


I made my New Year's resolutions on at the beginning of the year. And and just a week past since then. I got stuck.
I have two small children, and recently the childcare center was't open because of the New Year vacation. Spending all day with small children needs lots of energy. Also, my daughter is at a rebellious age.
I try to study ( and exercise) after they fell fall asleep, but I am too tired to do so. My battery is completely dead.
I feel impatient with myself.
But at the same time, I know the importance to not to give up (this needs some small changes; see 4) below). I should try to keep improving even just a little.

A few points:

1) With "Study English and Spanish every day" and "Doing exercise to stay in shape" there is no consistency in tense (possibly aspect rather than tense). It would be better to say "Study English and Spanish every day" and "Do exercise to stay in shape" OR "Studying English and Spanish every day" and "Doing exercise to stay in shape"

2) Some people may disagree but I don't like starting a sentence with the word "and" or the word "but". Likewise, I do not follow a comma with "and" or "but".

3) "childcare center" is fine but, being British, I prefer the spelling "centre".

4) "... I know the importance of not giving up" or "... I know it's important not to give up".

I've rewritten the whole passage below with the corrections plus a few extra changes I've made for personal stylistic reasons:

I got stuck X(

1. Study English and Spanish every day 
2. Do exercise to stay in shape

I made my New Year's resolutions at the beginning of the year and just a week since then I have got stuck.
I have two small children and recently the childcare centre was't open because of the New Year's vacation. Spending all day with small children requires lots of energy. Also, my daughter is at a rebellious age. 
I try to study (and exercise) after they fall asleep but I am too tired to do so. My battery is completely dead.  
I feel impatient with myself but, at the same time, I know the importance of not giving up. I should try to keep improving even if it's just a little bit at a time.

お疲れ様です